Physics 3rd Secondary chapters (1-7)

Mr.Ahmed hekal

Mr. Ahmed Hekal

Chapter 1 A.Definitions

1- Electrical current: - Electrons movement through a conductor from negative pole to positive pole in the presence of electric

source2- Traditional Electrical current:

- Movement of positive charges through a conductor from positive pole to negative pole3- Current intensity:

- Quantity of electrical charges through a section of a conductor in 1 second4- Ampere:

- Current intensity results in passing quantity of charges of 1 Coulomb through a conductor in 1 second5- Coulomb

- The quantity of electrical charges that when passes through a conductor in time of 1 second it generates current of 1 Ampere

6- Potential difference:- The work done in joule used to transfer quantity of charges of 1 C between 2 points

7- Volt:- The potential difference bet. 2 points when work done of 1 J used to transfer quantity of charges of 1 C

8- Electromotive Force:- The whole work done outside and inside the battery to transfer 1 coulomb of charges in the electrical circuit- Potential difference between the poles of the battery in case of open circuit

9- Electrical Resistance:- The opposition الممانعةto the flow of the current- The ratio between potential difference in volt across the terminals of conductor and current intensity that

flows through this conductor in ampere10- Ohm’s Law:

- At constant temperature, current intensity is directly proportional with potential difference 11- Ohm:

- The resistance of conductor that allows passage current of 1 Ampere when potential difference across terminals of this conductor is 1 volt

12- Resistivity:- It’s the resistance of conductor of length 1 m and cross sectional area of 1 m2 at constant temperature

13- Conductivity:- The reciprocal of resistivity - Reciprocal of resistance of conductor of length 1 m and cross sectional area of 1 m2 at constant temperature

14- Kirchhoff’s first low:- In a closed circuit, summation of currents entering a point is equal to summation of currents exiting this

point- The algebraic summation of currents in a specific point in closed circuit equals zero

15- Kirchhoff’s second law:- Algebraic summation of e.m.f. in a closed circuit equals the algebraic summation of potential differences in

this circuit- Algebraic summation of potential differences in a closed branch equal zero

1

Mr. Ahmed Hekal

B.What’s meant by? 1- Current intensity passes through a conductor is 5 A

- The quantity of electrical charges that passes through a section of this conductor in 1second equals 5 coulombs2- Potential difference between terminals of a conductor is 20 V

- The work done to transfer 1 C of charges bet. terminals of this conductor is 20 Joule3- Electromotive force of a battery = 1.5 V

- The whole work done outside and inside the battery to transfer 1 coulomb of charges in the circuit = 1.5 joule4- Electrical Resistance of a conductor 100 Ohm

- The ratio between potential difference across the terminals of conductor and current intensity that flows through this conductor is 100 V/A5- Resistivity of a conductor = 6 *10-6 ohm.m

- Resistance of a conductor of this material of length 1 m and cross sectional area of 1 m2 at a constant temp. is 6 *10-6 ohm 6- Conductivity of material is 5.6 *107 ohm-1.m-1

- Reciprocal of resistance of conductor of length 1 m and cross sectional area of 1 m2 at constant temperatureIs 5.6 *107 ohm-1

C. Deductions 1- Resultant resistance of group of resistances connected in series

- Current intensity is constant through all resistances - Potential difference is divided between them

V = V1 + V2 + V3

V = I RI R` = I R1 + I R2 + I R3

Then

2- Resultant resistance of group of resistances connected in parallel- Potential difference is constant across all resistances- Current intensity is divided between resistances

I = I1 + I2 + I3

I = V / RV / R` = V / R1 + V / R2 + V / R3

Then

2

R` = R1 + R2 + R3

1 / R` = 1 / R1 + 1/ R2 + 1 / R3

Mr. Ahmed Hekal

D. Factors that depends on Physical quantity Factors that this quantity depends on

Resistance of a conductor R = Ꝭe L/A

1- Length of conductor (directly proportional)2- Its cross sectional area A (inversely

Proportional)3- Material type of this conductor4- Temperature of this conductor

Resistivity of conductor 1- Material type of this conductor2- Temperature of this conductor

Conductivity of a conductor 1- Material type of this conductor2- Temperature of this conductor

F.Comparisons

resistances connected in series resistances connected in parallelShape of connection

Target

To obtain a large resultant resistance from a group of small resistances

To obtain a small resultant resistance from a group of large resistances

Current intensity Equal or constant in all resistances The whole current equals the summation of all currents in all resistances

Potential difference The whole P.D. equals the summation of all P.D.s in all resistances

V = V1 + V2 + V3

Equal or constant across all resistances

Law of resultant

If all resistances are equal

R` = N RWhere N is number of them

R` = R / N

3

R` = R1 + R2 + R3 1 / R` = 1 / R1 + 1/ R2 + 1 / R3

Mr. Ahmed Hekal

E.What Happens in these cases 1- Increasing potential difference to double value for current intensity and power consumed?

- Current intensity will increase to double as I = V / R- Power will increase 4 times as Pw = V2 / R

2- Current intensity increases to double for the resistance value- Resistance remains constant as it doesn’t depends on current it depends on - Length of conductor (directly proportional)- Cross sectional area A (inversely Proportional)- Material type - Temperature

3- Increasing cross sectional area of a conductor to double and decreasing its length to half value for the resistance- L1 = 2 L , L2 = L , A1= A , A2 = 2 A- R1 / R2 = L1 A2 / L2 A1 = 2 L * 2 A / L * A - R2 = ¼ R1

4- Connecting two resistance in parallel on of them has a value of 1 ohm to the resultant resistance- Resultant resistance will be less than 1 ohm

5- Current doesn’t flow from an electric source to potential difference between the terminals of this electric source- Potential difference between the terminals of this electric source will be equal to electromotive force of the

electric source according to this relation

(V = VB – I r) and I = 0 then V = VB

F.Give reason 1- Work should be done to transfer charges from point to point

- To get rid of resistance bet. the two points and current can flow2- Some materials can conduct electricity but others cannot

- As some materials have a plenty of free electrons so it allows flow of current while other materials don’t have free electrons or their electrons are strongly correlated to their atoms3- Increasing radius of a wire of copper leads to decreasing its resistance to quarter value

- According to this relation R = Ꝭe l/r2

Resistance is inversely proportional with square of radius 4- When a conductor is shaped to be parallelogram its ribs resistances are different while if shaped as a

cube its ribs resistances are equal- As ribs of parallelogram are different in length so their resistance differs according to relation

R = Ꝭe l/A but cube ribs are equal in length and equal in resistance5- Resistance increase when increasing temperature

- When raising temperature this increase the speed of vibrating its molecules and increase the rate of collisions between electrons of current and conductor molecules so the opposition الممانعة of current increases6- Resistivity of a conductor is a physical property

- As it depends on the type of the conductor material at constant temperature

4

Mr. Ahmed Hekal

7- Conductivity of a conductor is a physical property

- Because conductivity is the reciprocal of resistivity which depends on the conductor material at constant temperature8- Conductivity factor of copper is large

- As resistivity of copper is very small in cause of plenty of free electrons in copper9- It’s preferred to use wires of copper in the electrical connections

- As resistivity of copper is very small so its resistance is low and this prevent wire from consuming electrical energy10- Home devices are connected in parallel

- All devices will work on the same potential difference of the source so each device can work alone and if one of them damaged it doesn’t affect the others and also to decrease their total resistance which doesn’t affect the main current11- Home devices aren’t connected in series

- Because potential difference will be divided across them which leads to a probability of insufficient voltage on a device that cannot operate and one device cannot work alone also their total resistance will be huge which prevents the current from passing through the circuit12- The electrical power increases in case of connecting two resistance on parallel

- When connecting resistances in parallel their total resistance decreases and current will increase and Power also will increase according to this law Pw= IV 13- In a circuit of parallel connection resistances we use thick wires at the terminals of battery and thin

wires at the terminals of each resistance- As current intensity should be maximum at the input and output of the battery so we use thick wires of low

resistance while current is divided through each resistance so we can use thin wires in terminals of each resistance14- Potential difference between battery poles increases when increasing resistance of its circuit

- According to this relation (V = VB – I r) when increasing resistance current will decrease and the internal potential difference (I r) will decrease and because VB is constant then potential difference across the battery will increase15- E.M.F of a battery is larger than potential difference between its outer terminals when closing the

switch- Because the internal resistance of the battery consumes power to allow current to flow inside it so

(VB = V + I r) so VB > V

5

Mr. Ahmed Hekal

6

LawsTo compare between Power consumed in two resistancesWhen V is constant (Pw)1 / (Pw)2 = R2 / R1

When current is constant(Pw) 1 / (Pw)2 = R1 / R2

ResistanceR = V / IR = Pw / I2 R= V2/Pw

R = Ꝭe L/A = Ꝭe L/r2

Ꝭ (density) = m (mass) / v (volume) = m / vꝬ

And v = L * A and L = v / AThen = m / L A then ꝬA = m / L and ꝬL = m / A ꝬR = Ꝭe L2 / mꝬR = Ꝭe v (volume) / A2

R = Ꝭe L2/ v (volume)Compare between resistancesR = Ꝭe m / Ꝭ A2

R1/R2= Ꝭe1 L1 A2 / Ꝭe2 L2 A1

R1/R2 = Ꝭe1 Ꝭ1 L12 m2 / Ꝭe2 Ꝭ2 L2

2 m1

R1/R2 = Ꝭe1 L1 r22 / Ꝭe2 L2 r1

2

Conductivity

σ = 1 / Ꝭe= L / R A

LawsQuantity of charges

Q = I t

Q = n qe

Q = W / V

Q: total quantity of charges (electrons)

n: number of electrons

qe: charge of one electron

W: work done

V: potential difference

I: current intensity

t: time

Potential difference V

V = W / Q

V = W / nqe

V = I R

V = Pw / I

Current IntensityI = Q / tI = n qe / tI = V / RI = Pw / VElectrical Power Pw = W / tPw = V I Pw = I2 RPw = V2 / R

Mr. Ahmed Hekal

To Solve Kirchhoff’s Problems follow the following:

7

Mr. Ahmed Hekal

1- Divide the circuit to no. of loops (2 or 3 loops)2- Find a point (junction) in which all currents are entering or leaving it3- Write the first equation using Kirchhoff’s first law (sum of currents entering a point equals to sum o

currents leaving this point 4- Specify my direction as follow

A. If there is one battery in the loop, specify the direction to be from +ve pole to –ve pole of this battery

B. If there are two batteries in the loop, specify the direction to be from +ve pole to –ve pole of the largest battery

5- Write the 2nd and 3rd equations using Kirchhoff’s second law (sum of potential difference inside a loop equals zero), we have two choices:A. If there is one battery in the loop, then write its value direct V= IR + IRB. If there are two batteries in the loop, then we have two choices

If they are connected parallel ( -ve connected to –ve and +ve connected to +ve) then subtract their values V1-V2 = IR +IR

If they are connected in series ( -ve connected to +ve and +ve connected to negative)Then add their values to each other V1+V2= IR +IR

C. The sign of IR depends on the direction of the current If the current passes in the same direction of my direction then put it in +ve (+IR) If the current passes in the opposite direction of my direction then put it in –ve (-IR)

6- Current that leaves the battery is the same current enters the battery7- Potential difference between two points is equal to the potential (or voltage) at the point of higher

potential the potential (or voltage) at the point of lower potential8- Solve the 3 equations using calculato

Chapter 28

Mr. Ahmed Hekal

G. Definitions 16- Magnetic Flux:

- Number of magnetic field lines of a magnet from north pole to south pole 17- Magnetic flux density at a point:

- It’s the magnetic flux for unit area which is normal to magnetic lines around this pointOr- The magnetic force affecting a wire of 1 m length placed normal to magnetic flux and a current of 1 A

passes through it18- Tesla

- The magnetic flux density that generates a force of 1 Newton on a wire of 1 m length and a current of 1A passes through it when this wire is normal to the flux lines

19- Permeability coefficient of a medium: - The ability of medium to permit the magnetic flux through it

20- Dipole Moment :- It’s the magnetic torque affecting a coil placed parallel to magnetic field of 1 tesla when an electrical current

passes through it. 21- Moving Coil Galvanometer (sensitive Galvanometer):

- A device used to detect a very weak current to measure its intensity and determine its direction22- Galvanometer sensitivity:

- The deviation angle of its pointer from zero position when a current of 1 A passes through it 23- Shunt Resistance

- A small resistance connected in parallel with galvanometer to convert it to an ammeter to measure higher currents

24- Ammeter Sensitivity- Ratio between maximum current measured by galvanometer to maximum current measured after

converting it to ammeter25- Multiplier Resistance:

- Large resistance connected in series with galvanometer to convert it to voltmeter to measure higher voltages

H. What’s meant by? 7- Flux density at a point is 0.4 Tesla

- It means that a magnetic force of 1 N is affecting a wire of 1m length placed normal to the magnetic flux at this point and a current of 1 A passes through it 8- Dipole Moment is 0.7 N.m/T

- It means that magnetic torque of 0.7 N.m is affecting a coil when a current passes through it and this coil is placed parallel to a magnetic flux of 1 tesla

I. Figures J. Conditions needed to :

9

Mr. Ahmed Hekal

Attraction force bet. two wires having currents pass through them

The two currents should be in the same direction

Repulsion force bet. two wires having currents pass through them

The two currents should be in opposite directions

Flux density vanishes at a point between two parallel wires having currents pass through them

The two currents should be in the same direction

Neutral point exists between two straight parallel wires in a mid-point between them

The two currents should be equal values and in the same direction

Impossibility of existence of a neutral point for two straight parallel wires having currents pass through them

The two currents are equal values and are in opposite directions

Vanishing the Force affecting a wire have a current pass through it inside a magnetic field

Wire is parallel two to the magnetic flux

Vanishing the torque affecting a coil in which a current passes and is placed in a magnetic field

When the plane of the coil is perpendicular to the magnetic flux

K.Devices Device Usage Scientific Idea and explanation

Moving Coil Galvanometer to detect very low DC currents and measures its values and determines its direction

Idea:The torque affecting a rotating coil having a current passes through it inside a magnetic fieldExplanation:When current passes through the coil, two equal parallel forces are generated in opposite directions on two ribs ضلعين of the coil which causes rotation torque on the coil

Shunt resistance in Ammeter Converts the galvanometer to Ammeter to measure higher currents

When a small resistance is connected in parallel with the galvanometer coil this leads to decreasing the total resistance of the ammeter which avoid affecting the current needed to be measured

Multiplier resistance in Voltmeter Converts the galvanometer to Voltmeter to measure higher potential differences

Connecting high resistance in series with a galvanometer leads to increasing the total resistance of it and when connecting this Galvanometer in parallel with the circuit it consumes a

10

Mr. Ahmed Hekal

very small current then it doesn’t affect the potential difference needed to be measured

L. Usages

Pair of spiral springs in Galvanometer 1- It’s used as connectors to current2- Control the pointer movement using reverse torque to

indicate the right value3- Return the pointer to its zero position

The concave poles in Galvanometer They remain the flux density constant in the space in which coil moves, this way ensures that flux lines are always in a radius form and they are parallel to the coil plane (normal to two certain rips)

Iron core inside Galvanometer Collecting and concentrating the flux lines inside the coil

Jeweled bearings in Galvanometer Coil stands on them and they facilitates its rotation

The standards and variable resistance in Ohmmeter

Controls the current intensity to be maximum value which moves the pointer to the end of reading (zero ohm) before adding the resistance needed to be measured

M.Deductions

1- Magnetic force that affects a wire through which electrical current passes in a magnetic field:-

- F α B (Flux Density) And F α I (current) And F α L (length affected in wire)- F α BIL

-

Where is the angle between the wire and the fluxNewton = Tesla.ampere.m, Tesla = Newton /ampere.m

2- Torque affecting a rectangle coil through which current passes and is placed inside a magnetic field

- when a coil is placed in a magnetic field and a current passes through it and the plane of the coil is parallel to the plane of the field

11

F = BIL sinNewton

Mr. Ahmed Hekal

- there are 2 rips are parallel to flux so force is zero, and the other 2 rips are perpendicular to the field so they are affected by 2 equal and opposite forces not on the same line, this will cause rotation

- rotation happened in cause of torque- Torque = force * distance- Force = BIL sin - Distance = L (the normal distance between the pole and the affected rip) this distance is the wide of the

rectangle- Torque = B I (Length* width) sin - Ʈ = B I A sin - If we have number of turns N in the coil so :

And

= B |md| sin

Where |md| is the dipole moment |md|= I A N

3- Shunt Resistance- Rs and Rg are connected in parallel so - Vg = Vs

- Then Ig Rg = Is Rs

- Rs= Ig Rg / Is but Is= I - Is

- Then

4- Multiplier Resistance Rm

- Rm and Rg are connected in series so - V = Vg + Vm = Ig Rg + Ig Rm

--

N. Factors that depends on

12

= B I A N sin

Rs= Ig Rg / (I - Ig)

Rm= (V – Ig Rg) / Ig

Mr. Ahmed Hekal

Physical quantity Factors that this quantity depends on

Magnetic Flux Density generated from wire at a point B = d )

1- Current Intensity (directly proportional)2- Distance bet. the point and wire (inversely

proportional)3- Permeability coefficient of the medium (directly

proportional)

Magnetic Flux Density generated from coil at the center point B = r)

3- Number of turns (directly proportional)4- Current Intensity (directly proportional)5- Radius of coil (inversely proportional)6- Permeability coefficient of the medium (directly

proportional)

Magnetic Flux Density generated from Solenoid at a point on its axis B = L

3- Number of turns (directly proportional)4- Current Intensity (directly proportional)5- Axis length (inversely proportional)6- Permeability coefficient of the medium (directly

proportional)

Magnetic ForceF = BIL sin

1- Magnetic flux density B (directly proportional)2- Length of affected part of the wire (directly

proportional)3- Angle between the field and wire (directly

proportional)4- Current Intensity (directly proportional)

Torque affecting a coil = B I A N sin

1- Number of turns (directly proportional)2- Current Intensity (directly proportional)3- Magnetic flux density B (directly proportional)4- Angle between the field and wire (directly

proportional)5- Area of the rectangular coil (directly proportional)

Dipole Moment |md|= I A N

1- Number of turns (directly proportional)2- Current Intensity (directly proportional)3- Area of the rectangular coil (directly proportional)

G. Comparisons

13

Mr. Ahmed Hekal

Two wires having a current passes through themIn the same direction In opposite directions

Resultant of flux density at a point in between

B total = B1- B2 where B1> B2 B total = B1+ B2

Resultant of flux density at a point outside them

B total = B1+ B2 B total = B1- B2 where B1> B2

Neutral Point B1 = B2 Falls between the two wiresI1 / (x-d) = I2 /d

Where x is the distance bet. Wires and d is the distance bet. the point

and wire of lower current

Falls outside the wiresI1 / ( x + d ) = I2 /d

Where x is the distance bet. Wires and d is the distance bet. the point and

wire of lower currentForce between the two wires Attraction Repulsion

- Rules

Ampere Right Hand Rule Right Screw Clock Rule Fleming Left Hand ruleFigure Straight wire Solenoid

Usage Specifying the direction of magnetic flux generated by a current passes through a wire

Specifying the polarity of the field

Specifying the direction of magnetic flux at center of a coil or solenoid axis

Specifying the pole type (North-South) at the face of a coil or solenoid

Specifying the direction of magnetic force affecting a wire which placed perpendicular to a magnetic field and current passes through it

Working Method

Thumb finger refers to current and other fingers rounding the wire will refer to magnetic flux

Thumb refers to magnetic flux and other fingers rounding the solenoid will refer to the current

When screw rotates in clock-wise direction its rotation refers to the current and its movement direction refers to magnetic flux

If the direction of current in a specific face is clock-wise then this face is South pole and if anti-clock then it will be North pole

Middle finger refers to current ,index finger refers to magnetic flux then the thumb refers to the force

Notice: magnetic flux lines is directed from north to south outside the coil and from south to north inside the coil

Ammeter, Voltmeter, Ohmmeter14

Mr. Ahmed Hekal

Ammeter Voltmeter OhmmeterFunction Measuring high currents Measuring potential

difference bet. two pointsMeasuring resistance

Resistance connected on the galvanometer coil

Galvanometer coil is connected in parallel to small resistance called Shunt resistance Rs

Galvanometer coil is connected in series to large resistance called Multiplier Resistance Rm

Galvanometer coil is connected in series to standard resistance Rc and variable resistance Rv and a battery

Idea Of Work Torque affecting a coil that has a current passes through it, this coil is rotating inside magnetic field

Torque affecting a coil that has a current passes through it, this coil is rotating inside magnetic field

Depends on the inverse relation bet. current and resistance at constant potential difference

Law Rs= Ig Rg / (I - Ig) Rm= (V – Ig Rg) / Ig I = V / (Rg+ Rc+ Rv+Rx+r)

How it’s connected in circuit

In series In parallel Device terminals is connected to terminals of the external resistance

Graduation Regular as I α Regular as V α Not regular as I α R`+Rx)

Shunt and Multiplier ResistancesShunt Resistance Multiplier Resistance

Method of connection In parallel with galvanometer coil In series with galvanometer coilFunction Convert the galvanometer to Ammeter to

measure higher currentsConvert the galvanometer to Voltmeter to measure higher potential difference

Idea of work By connecting shunt resistance in parallel with the galvanometer this leads to reduce the total resistance of the device(ammeter) which avoid affecting the current needed to be measured

Connecting high resistance in series with a galvanometer leads to increasing the total resistance of it and when connecting this Galvanometer in parallel with the circuit it consumes a very small current then it doesn’t affect the potential difference needed to be measured

Analog Measuring devices Digital Measuring devices Its idea depends on Torque affecting a coil that

has a current passes through it, this coil is rotating inside magnetic field

Values are appeared on a graduation on which pointer is moving

As Galvanometer, Ammeter ,Voltmeter

Depends on digital electronics Values are appeared as digits displayed on the

screen of the device As devices of measuring DC and AC currents

O. What Happens in these cases 1- Current flows in the same direction in two parallel wires

15

Mr. Ahmed Hekal

- The resultant of flux densities outside the wires will be larger than it between the wires so attraction force is generated between them

2- Current flows in opposite directions in two parallel wires- The resultant of flux densities between the wires will be larger than it outside them so repulsion force is

generated between them3- Cutting a solenoid of length L and number of turns N at a middle point on its axis and connecting one half

to the same battery - The solenoid resistance is reduced to half and current intensity will increase to double (and number of turns

remain constant in unit length) so flux density will increase to double4- Placing wire having a current perpendicularly to a magnetic field- Wire is being affected by a magnetic force which is perpendicular to current direction and flux lines5- Passage of dc current of high intensity (bigger than Ig) through the galvanometer coil- high torque is generated in the coil which is higher than the moment of the ability of the two bearing coils

so they are destroyed and the device is broken down6- Passage of high frequency (AC) current inside galvanometer - The pointer is oscillating at the zero reading according to inertia as the pointer cannot react with the change

of direction7- Reducing the value of shunt resistance- Ammeter sensitivity is reduced and the graduation of reading is increased 8- Increasing the value of multiplier resistance - Voltmeter sensitivity is reduced and it will measure higher voltage9- Nonexistence of standard resistance- Galvanometer coil will be damaged if current is high and ohmmeter pointer will not be accurate

P.Give reason 1- It’s recommended in building to be far away the higher voltage towers

16

Mr. Ahmed Hekal

- To reduce the effect of the magnetic field which is harmful to the health and environment as the magnetic flux density is inversely proportional to the distance

2- The neutral point is positioned between two wires having currents pass through them in the same direction

- Wires will generate two opposite magnetic fields at all points between them so neutral point exists between them when they vanish each other

3- The neutral point is positioned outside two wires having currents pass through them in opposite directions

- Because of generating two opposite magnetic fields outside the wires so neutral point exists outside them when they vanish each other

4- Parallel wires are attracted when currents pass through them in the same direction- As the resultant flux density between them is lower than it outside them so magnetic force is generated

from the higher density region to lower density region so they are attracted5- Flux density increases on axis of solenoid that has current passes through it when placing iron

core inside it- Because permeability coefficient of iron is more than it in air so iron will increase and concentrate the

magnetic flux lines which leads to increase the density6- Magnetic field in a coil or solenoid may vanish although there is a current passes through it

- As the coil or solenoid is double rounded ,so the magnetic field of one direction is opposing the magnetic field of the second direction

7- Movement of a straight wire which has electrical current and placed normal to a magnetic field- This happens according to the difference between the original magnetic field and the field generated by the

wire so wire will move from high density to low density8- wire having current may not move although it’s placed inside magnetic field

- because it’s placed parallel to magnetic field so (= 0) and F = B I L sin which leads to zero9- when current passes through a solenoid and a wire placed on its axis, the wire is affected by

magnetic field - as the wires is placed parallel to magnetic field that is generated by passage of electrical current in the

solenoid

And F = B I L sin

10- torque may not be generated on a rectangular coil which has a current and placed into a magnetic field

- As the coil should be placed parallel to the magnetic field in order to be affected by magnetic force on two rips which generate the torque, so if it’s placed perpendicular to the field torque will be 0

11- Torque is reduced on the rectangular coil through its rotation starting from parallel position- At the parallel position the angle between the coil and the normal plane to field equal 90 so torque is

maximum, while rotating the angle is decreased until it reaches 0 at which angle is zerosin

12- Concave poles in Galvanometer - To keep the magnetic flux lines always parallel to the coils so at any position magnetic field density will be

constant and the deviation angle will always proportional to current intensity

13- Coil of galvanometer is connected to couple of bearings coils- They are used to

17

Mr. Ahmed Hekal

A. As connectors of current entering and exiting galvanometer B. They generate opposite torque used to

. Stop pointer at the right value of current

. Return pointer to zero value after the current disconnected

14- Coil of Galvanometer is placed on jewels bearings - To reduce frictions and maintain the equilibrium of coil to facilitate the rotation

15- Existence of iron core cylinder inside the coil of galvanometer- To concentrate and increase the magnetic flux inside the coil which increase the galvanometer sensitivity

16- Graduation of galvanometer is regular and zero reading is positioned in the middle- As the deviation angle is directly proportional with the current intensity and zero is positioned in the middle

to specify the direction of current17- Galvanometer cannot measure AC current

- As the magnetic field generated by AC is also alternating so the direction of torque changes each half cycle so inertia will prevent the reaction to this change

18- Galvanometer doesn’t measure high current intensities- As its coil cannot bear high currents because part of this current is converted to thermal energy which leads

to melting the coil wire and also the torque generated by higher current is very strong which may damage the jewels bearings

19- Ammeter is connected in series in the circuit- To measure the total current of the circuit

20- In Ammeter, a very small shunt resistance is connected in parallel with galvanometer coil- To reduce the total resistance of device which avoid current decrease and the majority of current will pass

through the shunt resistance which protect the coil from damage so we can use Ammeter in measuring high currents

21- Voltmeter is connected in parallel in the circuit- To make the potential difference across the voltmeter equal to the potential difference needed to be

measured 22- In Voltmeter, a very high multiplier resistance is connected in series with galvanometer coil

- To enlarge the resistance of the device so a very small part of current will pass through it and the majority of current will not affected so potential difference needed to be measured also will not affected

23- Electromotive force of the battery in Ohmmeter circuit should be constant- To maintain Ohm’s law and make the current always inversely proportional to resistance in case of

constant e.m.f24- High standard resistance is connected in Ohmmeter circuit

- To reduce the current passing through the circuit to protect the galvanometer coil from damage and make its pointer deviate to the maximum reading before connecting the unknown resistance

25- Graduation of Ammeter is regular and graduation of Ohmmeter is not regular- As in Ammeter the deviation angle is directly proportional to the current, but in Ohmmeter the current is

inversely proportional with the total resistance not only the unknown resistance 26- Ammeter graduation opposes the Ohmmeter graduation

- Because the current is inversely proportional with resistance so when adding resistance the current decreases

-

18

Mr. Ahmed Hekal

19

Laws2- Flux density in 2 coils

A. In the same level - Currents in the same direction

BT = B1+ B2 - Currents in opposite direction

BT = B1- B2 (B1>B2)B. Coils are normal to each other

- B = √B12

+ B22

3- Flux density between a coil and a wire

A. If the current is in the same direction- BT = Bwire+ Bcoil

B. If the current is in opposite directions- BT = Bbig- B small

4- To calculate number of turns in a coil

A. If a wire of length L is rounded in form of coil- N = L /2r

B. If the coil is less than 1 turn (part of a turn)- N = / 360

5- In case of the wire is tangent to the coil

- N I1 = I2/

6- If a coil of N1 turns is reformed to N2 turns and connected

- B1/B2 = N1r2/N2r1= N12/N2

2= r22/ r1

2

Laws1- Magnetic Flux m in straight wires

m = 0 when flux is parallel to area

m = B A when flux is normal to area

m = B A sin when flux is making angle with the area

If the flux rotates with angle from

Parallel position m = B A sin Normal position m = B A sin (90-

- If the current is in the same direction- Neutral Point between the wires

I1 / (x-d) = I2 /d

Outside the wires between the wires

BT = B1+ B2 BT = B1- B2 (B1>B2)

- If the current is in the opposite direction

BT = B1- B2 (B1>B2) BT = B1+ B2

- Neutral Point is outside the wires I1 / (x+d) = I2 /d

-

Mr. Ahmed Hekal

20

Laws7- Solenoid

- B = µ N I /L = µ n I

- If turns are tangent So: L = N*2 r`

- Where :n is the no. of turns per unit area and r` is the radius of solenoid

8- Solenoid and Coil Bwire/Bsolenoid = Lsoleoid / 2 rcoil

9- Force F = B I L Sin - Between two wires -

F = L /2d

- Force of two wires affecting third wire

F3= BT I3 L3

- When equilibrium

F = Fg

B I L = mg

10-Torque = B I A N sin is the angle between the coil and the normal plane to the magnetic field

Laws11- Galvanometer sensitivity ==Galvanometer sensitivity * number of divisions

12- Ammeter

- Shunt resistanceRs= Ig Rg / (I - Ig)- Ammeter ResistanceR`=Rg. Rs / (Rg +RS)- Ammeter SensitivityIg/Is = Rs/ (Rs+ Rg)

13- Voltmeter

- Multiplier Resistance

Rm= (V – Ig Rg) / Ig

- Voltmeter ResistanceR`= Rg+ Rm

14- Ohmmeter To modulate the OhmmeterImax. = V / (Rg+ Rc+ Rv+r)Rc: is the standard resistance After adding unknown resistance

I = V / (Rg+ Rc+ Rv+Rx+r)

Mr. Ahmed Hekal

Q. Experiments

1- Magnetic field due to a current passes through a straight wire1) Use iron filings sprinkled on a horizontal cartoon boards 2) Use a wire to penetrate the board vertically3) Use battery to pass a current in the wire4) You will notice that iron filings are aligned in circles around a wire

2- Torque produced in a coil placed in a magnetic field1) Rectangular coil abcd is placed parallel to a regular magnetic field 2) Ribs ad,bc are parallel to flux lines, so there is no force affecting them3) Ribs ab,cd are normal to flux lines so they are affected by two equal and opposite magnetic forces

equal B I L 4) As a result for these two forces a torque is generated so we noticed that coil will rotate in a

direction specified by using Fleming Left Hand rule for each force- Middle finger refers to the current- Index (forefront) finger refers to magnetic field- Thumb will refer to the force

5) Torque is specified by this relation

= B I Lab Lbc = B I A

When coil has N number of turns so:= B I A N sin

Where is the angle between the coil and the normal plan on the magnetic field

21

Mr. Ahmed Hekal

Chapter 3R.Definitions

1- Electromagnetic induction- The phenomena of producing induced e.m.f and induced current in a conductor as a result of

changing the magnetic flux that’s intersected by this conductor2- Lenz’s Rule :

- The induced current is in direction to oppose the change that is caused by it3- Faradays Law:

- Induced e.m.f produced in a coil by electromagnetic induction is directly proportional with the time in rate of change magnetic flux intersected by the coil and also with number of turns

4- Weber:- It’s the magnetic flux that is normally penetrating a coil of 1 turn and when it’s vanished gradually

in 1 second an induced e.m.f of 1v is generated in the coil5- Mutual induction

- The electromagnetic effect between 2 adjacent coils one of them has AC current which affect the other coil so an induced current is generated in the 2nd coil to oppose the change happened to it

6- Mutual induction coefficient:- It’s the induced e.m.f generated in a one coil when changing the current in the other coil by rate

of 1 A/S7- Self-Induction:

- It’s the electromagnetic effect happened in the same coil to oppose the changing of its current 8- self-induction coefficient:

- it’s the induced e.m.f generated in the same coil when its current changes by rate of 1 A.S9- Henry:

- It’s the mutual induction coefficient between 2 coils when current of one of them changes by rate of 1 A/S an induced e.m.f of 1v is generated in the other coil

Or

- It’s the self-induction coefficient of a coil when its current changes in rate of 1 A/S an induced e.m.f of 1v is generated in the same coil

10- Eddy Currents:- It’s induced currents generated in a metal core as a result of its motion inside a magnetic field or if

it’s exposed to a changing magnetic field 11- Generator (Dynamo)

- A device used to convert mechanical (motion) energy to electrical energy12- AC current:

- It’s the electrical current that changes its value and direction periodically with time- It’s the current that changes its value from 0 to max. and returns back to 0 in half cycle then it

reverses its direction and reaches the max. value in opposite direction then returns to 0 again in another half cycle

22

Mr. Ahmed Hekal

13- Effective value of AC current:- It’s the dc current intensity that generates the same amount of thermal energy that’s generated

by AC current in the same resistance in the same time - It’s the dc current intensity that generates the same electrical power that’s generated by the AC

current in the same resistance14- Transformer:

- A device used to step up or step down the alternating voltage15- Transformer Efficiency:

- It’s the ratio of secondary coil power to primary coil power- It’s the ration of the electrical energy produced in the secondary coil to the electrical energy

consumed in the primary coil in the same time16- Electrical Motor:

- A device used to convert electrical energy to mechanical (motion) energy

S.What’s meant by

T.Figures U.Conditions needed to :

Generating of directly induced e.m.f or directly induced current in the secondary coil

1- Moving the primary coil away from secondary coil

2- Decreasing the current in the primary coil3- Open the circuit of the primary coil while it is

near to or inside the secondary coilGenerating of inversely induced e.m.f or inversely induced current in the secondary coil

1- Moving the primary coil near to or inside secondary coil

2- Increasing the current in the primary coil3- Close the circuit of the primary coil while it is

near to or inside the secondary coilGenerating Eddy currents 1- Moving (rotating) a piece of metal core inside a

constant magnetic field 2- Exposing a piece of metal core to a variable

magnetic field Generating a unified directional current but variable in its value in Dynamo (Generator)

1- Replacing the two metal rings with one metal cylinder cracked into two halves this cylinder called current rectifier

Generating DC current in Dynamo (Generator) 1- Using several coils separated by small equal angles

2- Replacing the two metal rings with one metal cylinder cracked into several parts where No. of parts = double No. of coils

Improving the transformer efficiency 1- Fabricating the coils from metal wires which have

23

Mr. Ahmed Hekal

a very small resistance to reduce losing of electrical energy in form of heat

2- Fabricating the iron core from insulated slices of wrought iron as it has high resistivity used to reduce Eddy currents

3- The wrought iron is characterized by the ease of moving of its magnetic molecules it leads to reduce losing energy in form of mechanical energy

4- The secondary coil is rolled around the primary coil to prevent leakage تسرب of magnetic منعflux lines of primary coil away from the secondary coil

Improving efficiency of rotating the electrical motor(improving the torque of rotation)

1- Using several coils separated by small equal angles

2- Replacing the two metal rings with one metal cylinder cracked into several parts where No. of parts = double No. of coils

V.Applications of electromagnetic Induction

Device Usage Scientific Idea and explanationFluorescent Lamp Lighting Idea:

Self-induction in coilExplanation:the magnetic energy stored in the coil will be transferred to a vacuum tube which has inert gas خامل this energy causes غازcollisions between gas atoms so they are ionized and collide with the inner surface of lamp which is plated with fluorescent material so visible light is released

Induction furnaces Melting metals Idea:Eddy CurrentsExplanation:When changing magnetic that’s penetrated by an iron core, induced currents are produced in this core which leads to increase its temperature until melting degree

24

Mr. Ahmed Hekal

Dynamo (Generator) Convert mechanical (motion) energy to electrical energy

Idea:Electromagnetic InductionExplanation:When rotating the coil bet. magnet poles, it intersects variable number of magnetic lines so an induced e.m.f and induced AC currents is generated inside the coilAC current changes its value and direction gradually with time

Electrical Transformer 1- step up or step down the alternating voltage

2- reduce losing energy during its transfer from generators to consumption places through far distances

3- In some home devices

Idea:Mutual Induction bet. 2 coilsExplanation:When primary coil is connected to AC source, so the changing in magnetic field will generate induced e.m.f in the secondary coil that will be bigger than or smaller than e.m.f of source according to number of turns in the two coils It enlarges the e.m.f when NP > Ns

It reduces the e.m.f when NP < Ns

Electrical Motor Convert electrical energy to

mechanical (motion) energyIdea:Torque results in passage of electrical current in a coil inside a magnetic fieldExplanation:When electrical current passes through a coil, two equal and opposite directions forces will affect the two ribs normal to magnetic field so torque is generated which rotates the coil in one direction around its axis

W.Usages

Fleming’s Right Hand Rule Specifies the direction of induced current in a straight wire moves normally to magnetic field

Unified direction and variable intensity electrical current

Preparing some metals by electrical analysis of its compounds

Unified direction and unified intensity electrical current

Mobile phones chargers

Deductions 25

Mr. Ahmed Hekal

5- Faraday’s Law: Induced e.m.f produced in a coil by electromagnetic induction is directly proportional with the time rate of change in magnetic flux intersected by the coil and also with number of turns

e.m.f m / t and e.m.f NSo

-

m / t: change in magnetic flux with time, N: Number of turns of coil

6- Induced e.m.f in a straight wire - when a wire of length L moves with velocity V normally on a regular magnetic field of density B

An induced e.m.f is produced in the wire

e.m.finduced = m / t = B t

Where is the change in the area the wire moved through

- if it moves a distance of x so L x e.m.finduced = B L x / tAnd x / t = V

e.m.finduced = B L V

- And if wire makes angle with field so

7- E.m.f generated by mutual induction - When current intensity changes in the primary coil of rate 1 /t , and induced (e.m.f)2 is generated

in the secondary coil which is directly proportional with the rate of change in magnetic flux m /t- So (e.m.f)2 m /t - And m /t 1 /t - Then (e.m.f)2 /t

- Where is the mutual induction coefficient

8- E.m.f generated by self-induction - Induced e.m.f produced is directly proportional with the time rate of change in magnetic flux so

e.m.f m /t 26

e.m.finduced = N m / t

e.m.finduced = B L V sin

(e.m.f)2 = /t

Mr. Ahmed Hekal

- The time rate of changing in magnetic flux is directly proportional with time range of changing in current m /t /t So e.m.f /te.m.f = - L /t

- Where Lis the self-induction coefficient9- The induced instantaneous e.m.f. generated in Dynamo (Generator)

- When coil rotates with a linear velocity V, where the longitudinal ribs intersect the magnetic flux lines, so if the angle between the direction of linear velocity and the plane of magnetic field is then induced e.m.f generated in the each rib is

e.m.finduced = B L V sin

- And e.m.f in one turn (two ribs)

e.m.finduced = 2 B L V sin

V = distance / time = (circumference of circle for 1 rotation) / time for 1 rotation

V = 2 r / t and frequency f = 1 / t V = 2 r f take 2 f = V = r where is the angular velocity, r is radius of rotation and V is linear velocity

- e.m.finduced = 2 B L r sin - We can take ( 2 r L = A ) where A is the Area of coil (L is the length and 2r is the width)- e.m.finduced = B A sin - And if coil has number of turns = N- e.m.finduced = N A B sin

- = 2 = t =2 f t

= 2 f = t

27

e.m.finduced = N A B sin

e.m.finduced = N A B sin t

Mr. Ahmed Hekal

10- Relations for the electrical transformer A. Relation between the two e.m.f. of the two coils of ideal transformer and their number of turns

- When primary coil is connected to source and circuit of the secondary coil is open, an induced e.m.f is generated in the primary coil by self-induction which is

- VP = NP m / t 1) - When closing the secondary coil circuit, an induced e.m.f. is generated in the secondary coil by mutual

inductions because secondary coil intersects the flux lines of primary coil- VS = NS m / t 2) - We suppose there is no lose in magnetic flux then

Divide 2) by 1)

B. Relation between the two currents of the two coils of ideal transformer and their number of turns- We suppose that there is no energy lose in the transformer so

Energy consumed in the primary coil in a specific time = energy generated in the secondary coil in the same time

VP P t = VS S t

VP P = VS S

- Power input (primary coil) = Power output (secondary coil) VS / VP = P /S

And VS / VP = NS / NP

This means that the current intensity in any coil is inversely proportional with its number of turns

28

VS / VP = NS / NP

P /S = NS / NP

Mr. Ahmed Hekal

C.Factors that depends on

Physical quantity Factors that this quantity depends on

Induced e.m.f generated in a coil

1- Time in rate of change magnetic flux intersected by the coil2- Number of turns

Induced e.m.f in a straight wire

1- Flux Density2- Length of the wire3- Velocity of wire intersecting to flux4- Sin of angle between the wire and the field

Mutual coefficient between two coils

1- Permeability coefficient of medium2- Volume of the coils (length and are of each turn)3- Number of turns of the coils4- The distance between them

Self-induction of a coil 5- Geometric shape of the coil6- Number of turns7- Length of the coil8- Permeability coefficient of medium

The induced instantaneous e.m.f. generated in Dynamo (Generator)

1- Number of turns2- Magnetic Flux Density3- Area of the coil 4- Angular velocity that coil rotates with, or frequency of

rotation 5- Sin of angle between the coil and the normal plane of

the magnetic fieldConsumed energy in a wire E = I V t

1- Current intensity2- Potential difference3- Time of current passage

H. Comparisons

29

e.m.finduced = N m / t

e.m.finduced = B L V sin

e.m.finduced = N A B sin t

Mr. Ahmed Hekal

AC current DC currentHow it’s obtained AC Generator - DC generators

- Batteries and cellsCharacteristics 1- it changes its value and direction with

time2- can be transferred for long distances

without losing energy, by stepping up its voltage using transformers

3- can be converted to DC current

1- it’s constant in value and direction2- cannot be transferred because it lose

its energy in form of heat3- cannot be converted to AC current

Usage 1- Lighting2- Heating3- Operating machines

1- Lighting2- Heating3- Electrical plating4- Charging batteries

Step-up Transformer Step-down TransformerUsage Raising voltage at generating stations Step-down voltage at consumption places

Number of turns NS > NP NP > NS

Electromotive Force Vs > VP VP > VS

Current intensity IP > IS IS > IP

Generator (Dynamo) Motor Transformer30

Mr. Ahmed Hekal

Usage convert mechanical (motion) energy to electrical energy

A device used to convert electrical energy to mechanical (motion) energy

1- step up or step down the alternating voltage

2- reduce losing energy during its transfer from generators to consumption places through far distances

3- In some home devicesStructure Rectangular coil of copper

wire rolled around core of wrought iron, the coil and core can be rotated easily and placed inside a magnetic field

Rectangular coil of copper wire rolled around core of wrought iron, the coil and core can be rotated easily and placed inside a magnetic field

Two coils (primary, secondary) are rolled around a core of wrought iron formed of insulated slices to avoid eddy currents

Operation Terminals of coil are connected to two split rings rotate with the coil and each ring touches a fixed graphite brush which connect the induced current of coil to external circuit

Terminals of coil are connected to two halves of a cracked cylinder, each half is connected to a fixed graphite brush, these brushes are connected to DC source (Cell)

Primary coil is connected to the source of AC current needed to raise or reduce its voltage VP

and secondary coil is connected to the external circuit that needs a specific value of voltage Vsf

D. Experiments

31

Mr. Ahmed Hekal

Experiment 1 Faraday’s ExperimentOR

- Experiment to generate induced current in a coilOR

- Experiment to convert mechanical energy to electrical energy

Steps and Notices

1- Connect terminals of coil of copper wire to a sensitive galvanometer which has zero in middle grade 2- Place a magnet inside the coil

Notice- Galvanometer pointer moves in a specific direction

3- Pull the magnet outside the coilNotice- Galvanometer pointer moves in opposite direction

4- Fix the magnet and move the coil near and far the magnetNotice- Galvanometer pointer moves in the two directions according to movement of the coil

Deduction - Results

An induced e.m.f and induced current is generated in a coil as a result of changing the magnetic flux around this coil (when intersecting the magnetic lines by the coil), the direction of this induced current depends on the movement direction of the magnet near or far the coil

- Experiment 2 Mutual induction between two coils Steps and Notices

1- Connect a coil to a circuit has (battery ,key and rheostat) to be the primary coil and connect another coil (secondary coil) to a galvanometer has zero in its middle graduation

2- Close the circuit of the primary coil and move it near to secondary coilNotice

- Galvanometer pointer moves in a specific direction3- Move the primary coil far away the secondary coil

Notice- Galvanometer pointer moves in opposite direction

4- Fix the primary coil inside the secondary coil and increase current intensity in the primary coilNotice

- Galvanometer pointer moves in a specific direction

5- Decrease current intensity in the primary coilNotice

- Galvanometer pointer moves in opposite direction

32

Mr. Ahmed Hekal

Deduction

We can generate induced e.m.f and induced current in a secondary coil by effect of a primary coil where

- Reverse induced e.m.f and reverse induced current : by increasing the magnetic field of primary coil so the induced current in the secondary coil is in direction to oppose the change causing it (in the primary coil) to resist the increase of magnetic field

- Directed induced e.m.f and directed induced current : by decreasing the he magnetic field of primary coil so the induced current in the secondary coil is in direction to oppose the change causing it (in the primary coil) to resist the decrease in the magnetic field

-

Experiment 3: self- inductionSteps and Notices

1- connect a coil of a strong magnet (of high number of turns) in series with (a battery of 6 volts, key) and in parallel with a lamp which works under voltage of 180 v

2- close the circuit

Notice- Lamp doesn’t work

3- Open the circuitNotice

- An electrical spark between the terminals of the key and lamp is lightening for a very short time

Deduction

1- When closing the circuit a reverse induced e.m.f and a reverse induced current is generated in the coil which delays the main current to reach its max. value and a strong magnetic field is generated in the coil because each turn is considered a small magnet

2- When opening the circuit the current is attenuated يضمحل (decreases) so an induced e.m.f and induced current is generated in the coil by self-induction this induced e.m.f is high because number of turns is big and the time rate of changing the current is also big e.m.f /t and induced current is high so it generates an electrical spark

E.Some Explanations 1- Specifying the direction of induced current using Lenz’s rule:

33

Mr. Ahmed Hekal

- When moving the north pole of a magnet near to a coil which has a current passes through it, the face of the coil which is near to the magnet will be also a north pole and an induced current will pass through the coil in the anti-clockwise direction to resist the change causing it N N

- When moving the north pole of a magnet far from a coil which has a current passes through it, the face of the coil which is near to the magnet will be a south pole and an induced current will pass through the coil in a clock-wise direction to resist the change causing it N S2- Fleming’s Right Hand Rule

Usage:

- Specifying the direction of induced current passing in a straight wire which moves perpendicular to a magnetic field

How it’s used

- make the thumb, index (forefront) and middle fingers are perpendicular, so - Thumb: refers to direction of movement- Index (forefront) : refers to magnetic field - Middle: refers to the induced current direction

3- Eddy currents disadvantages and how to avoid them :- Disadvantages: large part of electrical current is lost in thermal energy- How to avoid them? Made the iron core from thin insulated slices of silicon-wrought iron which has high

resistivity 4- Transformer Operation:

- The primary coil is connected to an AC source (needed to be transformed) and the secondary coil is connected to the external circuit which will use the transformed current

- When closing the circuit of the secondary coil and AC current passes through the primary coil, an alternating magnetic field is generated and the iron core will collect and concentrate it in the secondary coil turns

- An induced e.m.f and induced current is generated in the secondary coil which is larger or less than the source according to the ratio between number of turns in both coils5- How does Motor works along complete cycle

- In the first half cycle When the coil is parallel to the magnetic field its terminals (the two halves of cracked cylinder) touch the

graphite brushes, so current will pass through coil and two opposite forces acting on two ribs so they produce a torque causing rotation for the coil

Torque decreases gradually with the rotation of the coil until it vanishes when its plane is perpendicular to magnetic flux, but the coil continue rotating according to inertia until it returns back to its original position (parallel to the field)- In the second half cycle

Coil is parallel to the field so torque will be generated in the same direction so coil will continue rotation in the same direction

Torque decreases gradually until it vanishes , but the coil continue rotating according to inertia until it returns back to its original position (parallel to the field) this will happen each cycle

Current flows in the same direction in two parallel wires

34

Mr. Ahmed Hekal

F.What Happens in these cases 1- Moving a coil has electrical current near to another coil connected to a galvanometer

- A reverse induced e.m.f is generated in the second coil by the mutual induction2- Open an electrical circuit contains a magnetic coil connected in parallel with a battery

- An electrical spark happens across the key terminals3- Open the primary coil circuit when it’s inside the secondary coil

- A direct induced e.m.f. is generates in the secondary coil to resist the shortage in the primary coil current4- Increasing value of current in the primary coil placed inside a secondary coil which is connected to a

galvanometer - Galvanometer pointer deflects in one directions because of generating reverse induced e.m.f. on the

secondary coil by mutual induction5- A high frequency current passes through a coil rolled around a piece of metal

- Its temperature will increase according to eddy currents6- Growth of current in a coil rolled on a wrought iron core inside it to the time of current growth

- The time of current growth will increase in the coil as a result of generating a big reverse induced e.m.f because permeability coefficient of wrought iron is high and self-induction coefficient of it will be also high

7- Wires of electrical resistance are doubled rolled- Self-induction will vanish so the main current will be only affected by Ohmic resistance, because the

magnetic field produced by on turn will cancel the magnetic field produced by the next turn8- Increasing number of turns of dynamo to double and number of cycles in 1 second to double

- Induced e.m.f. will increase 4-times9- Increasing number of turns of Dynamo coil to double and decreasing its angular velocity 4 times

- Instantaneous induced e.m.f. will be reduced to half10- Replacing the two split rings of Dynamo with cylinder cracked to 2 halves

- AC current will be converted to unified direction current of alternating values 11- Dividing the cracked cylinder in Dynamo to number of pieces equal double number of coils

- This will completely convert the AC current to DC current which is unified in direction and constant value12- Connecting primary coil in a transformer with a cell (battery)

- The magnetic flux resulting on it will be constant so, no mutual induction will happen between the coils and the transformer will not work

13- Opening circuit of secondary coil in the transformer and connecting its primary coil with an AC source- A reverse induced e.m.f. is generated in the primary coil, it’s equal to e.m.f. source so current is approximately

zero14- Transferring AC current for long distances without raising voltage before transfer

- A lot of energy is lost in the wires in form of thermal energy

Give reason

35

Mr. Ahmed Hekal

1- An induced e.m.f. is generated in a wire moves normally on magnetic flux lines- Because the magnetic flux affects the free electrons of the moving wire so these electrons will release from

one terminal of the wire(+ve terminal) to another terminal (-ve terminal) so a potential difference is produced between the two terminals of wire

2- Induced e.m.f may not be generated in a moving wire in a magnetic field- Because the direction of wire movement is parallel to the magnetic flux lines, so according to law

e.m.finduced = B L V sin angle between field and wire will be 0 and e.m.f. will be zero

3- Induced e.m.f. produced in a coil is higher if the core of the coil is made of wrought iron- As the wrought iron has a higher permeability coefficient and this will increase concentration of magnetic

flux lines that are intersected by the coil which leads to increase the induced e.m.f4- Wires of standard resistance are double rolled

- To avoid the self-induction because the magnetic field produced by a turn is cancelled by the magnetic field produced by the next turn, so current will only affected by the Ohmic resistance

5- A piece of wrought iron doesn’t magnetized if it’s caught by double rolled wire has a current passing through it- Because the direction of current in the first wire opposes the direction of current in the second wire so

magnetic field generated by one of them will cancel the other, so resultant magnetic field equals zero6- The direct e.m.f. induced in a coil by self-induction always bigger than the reverse induced e.m.f

- Because the collapse rate of current is always bigger than the growth rate of current 7- Current intensity doesn’t reach maximum value in coil in the moment closing the circuit, and doesn’t vanish

also in the moment of opening the circuit, it takes time - This happens because of generating a reverse e.m.f. in the moment of closing and opening the circuit this

reverse e.m.f will oppose the main current whether when it increases or when it decreases 8- Current is growing in a straight wire faster than a coil

- Because the magnetic field produced around the wire is not intersected by the wire itself so there is no reverse induced current produced in it, but in case of coil the magnetic field produced in coil is intersected by the coil itself so a reverse induced e.m.f is generated in coil by self-induction and also a reverse induced current so it resist the main current in the coil

9- Vanishing the induced current in a straight wire is faster than it in a coil of air core which is faster than it in a coil rolled on an iron core- There is no reverse induced e.m.f generates in the wire because the wire doesn’t intersect its magnetic field- In the coil of air core, there is a reverse induced current is generated in coil to oppose the shortage in

current its value is high- In the coil of iron core, the reverse induced current is higher because the magnetic field is bigger than it in

the coil of air core according to the permeability coefficient10- When opening circuit of electrical magnet there is a spark appears in the position of cutting the current

- Because the rate of vanishing the current is very high so the rate of changing the magnetic flux is very high which leads to generating high induced current in the same direction of the main current to oppose its shortage

11- When AC current passes in a coil rolled on a piece of metal its temperature increases- Because of the eddy currents produced in it which leads to melt the metal

36

Mr. Ahmed Hekal

12- Eddy currents don’t produced in a fixed piece of metal otherwise the magnetic field around it is variable- As in the variable magnetic field, the magnetic flux lines intersected by the metal is changing so eddy

currents are generated13- Temperature of an iron cylinder is raised if it’s rolled by a coil connected to AC source

- As the AC current changes its value and direction periodically, so the magnetic field resulting by it is also changing, so eddy currents are produced in the cylinder

14- Induced e.m.f in the Dynamo (generator) coil is max. value when its plane is parallel to the magnetic field - According to this relation

e.m.finduced = N A B sin is the angle between the coil and the normal plane to the magnetic field so in this case equals 90 soValue of e.m.f will be maximum = N A B

15- E.m.f (average) in Dynamo through ¼ cycle = E.m.f (average) in Dynamo through ½ cycle

e.m.finduced = N m / t

In ¼ cycle: m = BA , t = ¼ T e.m.f = 4 N B A FIn ½ cycle: m = 2 BA , t = ½ T e.m.f = 4 N B A F

16- E.m.f (average) in Dynamo coil through a complete cycle = 0- As the average value of e.m.f in one direction( ½ cycle) is equal to average value of e.m.f in the opposite

direction (in the second ½ cycle) so the resultant equal zero17- the cracked cylinder in dynamo produce a unified direction current

- when coil is rotated in half cycle their terminals rotate with it and the current will pass in the same direction in the external circuit when touching the graphite brushes

18- Terminals of Dynamo coils are connected to number of cracked pieces which is double number of coils - To guarantee that brushes are always touched to the coil which is parallel to the magnetic field to finally

produce a current of constant value DC current19- The core of transformer is made of slices of wrought iron which are insulated

- Permeability coefficient of wrought iron is high so it helps in concentrating the magnetic flux lines - Resistivity of wrought iron is high and when it’s made of insulated slices, this will increase its resistance to

resist the eddy currents and reduce the energy loss in form of heat20- In Ammeter or Galvanometer the iron core is NOT divided into insulated slices

- Because Ammeter and Galvanometer used to measure dc currents, so there is no eddy currents are produced in the core , no change is happened in the magnetic flux

21- Transformer coils are made of copper wires- Because its resistivity is very low so the coils resistance is very low which avoid energy loss in form of heat

22- There is no transformer with 100% efficiency- Because there is energy loss in forms of:

A. Loss in magnetic flux lines from primary coil to secondary coil37

Mr. Ahmed Hekal

B. Loss in heat through the wiresC. Mechanical energy according to the movement of the iron core magnetic molecules

23- Transformers are not used in step-up or step-down a DC e.m.f.

Or Transformers don’t work if the primary coil is connected to DC source

- Because the magnetic flux produced by the DC current is constant so no induced e.m.f is produced in the secondary coil by mutual induction (there is no mutual induction happens)

24- Transformer doesn’t consume power when opening circuit of secondary coil, although its primary coil is connected to electrical source- When opening the secondary coil circuit a reverse induced e.m.f. is produced in the primary coil (by self-

induction) and it’s equal to e.m.f (source) so there is not potential difference and there is no current passes in the primary coil and no power is consumed

25- Transformer works when closing its secondary coil circuit- When closing secondary coil circuit, current passes through it, the magnetic flux resulting by it will be

intersected by the primary coil and it vanishes the reverse induced current in it, so the current of source will pass through the primary coil and continue working

26- Electrical energy is transferred from generators stations to consumers under a high voltage and low current- To reduce the consumed energy in the wires because power is directly proportional with square of current

intensity 27- Use of step-up transformers at the generating stations

- Because the step-up transformers raise the voltage at the generating stations which leads to reducing the current intensity in the transformer and this is useful in avoiding loss in energy consumed in transferring wires

28- The step-up transformers are current step-down and vice versa- Because the power is constant and this makes the voltage inversely proportional with current

V = Pw/ I

29- Motor continue in rotation although it passes through the position which is normal to magnetic field Or

The coil of electrical motor doesn’t stop when the graphite brushes touches the insulation part of the cracked cylinder halves

- Because the inertia makes the coil to continue rotating and the two halves exchange their positions and also current exchange its direction so torque will be in the same direction

30- To increase Motor power, we use several coils separated by small angles- To increase the torque by guarantee that the coil is always parallel to the magnetic flux so the torque is

always maximum value an coils rotates with high angular velocity, this leads to enhance the motor efficiency

38

Mr. Ahmed Hekal

39

LawsE.m.f in Dynamo (Generator)

A. Instantaneous e.m.f. e.m.f = e.m.fmax. Sin

e.m.f = N A B sin t

V / r = t = 2T = 2 f inside (sin) = 180outside (sin) = 22/7

B. Maximum e.m.f. E.m.f max. = N A B

C. Effective e.m.f.

E.m.f effective = e.m.fmax. Sin 45

D. Average e.m.f.

In ¼ cycle and ½ cycle

e.m.f = 4 N B A F

In ¾ cycle

e.m.f = 4/3 N B A F

In 1 cycle

e.m.f = 0

Instantaneous induced currentInstantaneous = IMAX sin

Number of reaching the AC current to maximum value in 1 second= 2 f

Number of reaching the AC current to zero in 1 second = 2 f +1

LawsFaraday’s Law e.m.finduced = N m / t

- If area changed

e.m.finduced = N B / t

- If flux density changed

e.m.finduced = N B / t

- If coil rotates

A. ¼ cycle (90) e.m.finduced = N B / t

B. ½ cycle (180) e.m.finduced = 2 N B / t

C. 1 complete cycle e.m.finduced = because m=0

E.m.f. induced in a coil

Self-induction:

e.m.f = - L /t = N m / t

(Self-induction coefficient)

L = / L (length)

Mutual Induction

(e.m.f) 2 = /t = N2 (m )2/ t

Mr. Ahmed Hekal

40

LawsElectrical Transformer

A. Ideal Transformer:

VP P t = VS S t VS / VP = P /S

P /S = NS / NP

In case of 2 secondary coils:

(Pw) p = (Pw) s1 + (Pw) s2

B. Non-Ideal Transformer:

ɳ = (Vs Is/VP Ip) * 100

ɳ = (Vs Np/Vp Ns) * 100

(Pw) p > (Pw) s

Pw (consumer) = Pw (station) - Pw (loss in wires)

1- Power at generating stations = I V

2- Power consumed in wires = I2 R

3- Shortage in Volt = I R

LawsElectrical Motor

A. Current Intensity - Before operation

I = e.m.f. (source)/ R- During Running

I = e.m.f. (motor)/ R

B. Electromotive force

E.m.f motor = e.m.fsource – e.m.freverse

Mr. Ahmed Hekal

Chapter 4X.Definitions

1- AC current- It’s the current that changes its magnitude gradually from 0 to maximum after quarter cycle and

changes its direction after half cycle2- AC frequency :

- It’s the number of complete cycles of AC current in 1 second3- Periodic Time of AC:

- It’s the time taken by AC current to make a complete cycle4- Hot Wire Ammeter:

- Device used to measure AC or DC current and it depends on the expansion of a wire made of alloy of platinum and iridium by the thermal effect of electrical current

5- Inductive Reactance:- It’s the resistance of a coil caused by its self-induction X l

6- Electrical Capacitor:- Two parallel insulated metal plates, used to store electrical energy in form of electrical field

7- Capacitance: - The ratio between the charge placed on one plate and the potential difference between the two plates

8- Capacitive Reactance:- It’s the resistance of a capacitor caused by its capacitance Xc

9- Farad:- It’s the capacitance of a capacitor that ,if it’s charged by a charge of 1 coulomb the potential difference

between its plates is 1 volt10- Impedance:

- It’s the equivalent for the ohmic resistance, inductive reactance and the capacitive reactance for an AC circuit

11- Oscillator Circuit:- It’s an electrical circuit in which there is an exchange for energy stored in inductive coil in form of

magnetic field and the energy stored in a capacitor in form of electrical field12- Resonant Circuit :

- It’s an oscillator circuit contains a resistance, inductive coil, capacitor and AC source and it only allows passage of AC current has frequency equal or very close to its frequency

41

Mr. Ahmed Hekal

Y.What’s meant by 1- AC frequency is 50 Hz

- it means that number of complete cycles that made by AC current in one second is 50 cycles2- Periodic Time of AC current is 0.02 second

- This means that time taken by AC current to complete 1 cycle is 0.02 second3- Inductive reactance of coil is 100 ohm

- It means that the resistance for the coil resulting in its self-induction is 100 ohm4- Capacitance for a capacitor is 5 micro-farad

- It means that the quantity of charges placed on one plate is 5 *10 -6 coulombs when the potential difference between is plates is 1 volt

5- Capacitive reactance is 100 ohm- It means that the resistance of the capacitor according to its capacity is 100 ohm

6- Impedance is 50 ohm- it means that the equivalent resistance for (ohmic resistance. Inductive reactance, capacitive reactance)

is 50 ohm7- Phase angle for a circuit has inductive coil and resistance is 45o

- It means that the total voltage leads current by angle 45o

Tan = VL/VR = XL/R = 1 , XL =R, VL=VR

8- Phase angle for a circuit has capacitor and resistance is 45o

- It means that the total voltage lags current by angle 45o

- Tan = - VC/VR = -XC/R = - 1 , XC =R, VC=VR

9- Resonant circuit frequency is 104 Hz- It means that the oscillator circuit frequency equals source frequency = 104 Hz and it only allows the

current of this frequency to pass through it and inductive reactance equals the capacitive reactance only at frequency 104 Hz

Z.Devices

Device Usage Scientific Idea and explanation1- Hot Wire Ammeter Measures the effective value of AC

current and it also measures DC current

Idea:Thermal effect of electrical currentExplanation:When current (DC or AC) passes through an ohmic resistance it generates a quantity of heat which depends on the effective value of this current

2- Antennas Radio channels Idea:Resonance circuitExplanation:When we change the channel on radio device, the frequency of the resonance circuit changes to a specific value which equals the frequency of the desired channel current (because electromagnetic wave of the channel is

42

Mr. Ahmed Hekal

converted to AC current)

AA. Usages

1- Platinum-Iridium Wire It’s heated up and expands when electrical current passes through it so we can measure the effective value of current

2- Silk thread in Hot-Wire Ammeter It is pulled by the platinum-iridium wire so the roller will rotates and pointer will move and stops on the effective value of the current

3- The board on which the platinum wire is tensed

Get rid of zero error

4- Roller in Hot-Wire Ammeter It rotates when it’s pulled by the silk thread, so pointer will deviate until it reaches the effective value

5- Coil in Hot-Wire Ammeter It pulls the silk wire to rotate the roller and move the pointer to the effective value of the current

6- The resistance connected to the platinum-Iridium wire

It divides the total current to allow a suitable current to pass through the wire

7- The variable-capacity capacitor in RLC circuit which works as resonant circuit

when changing the capacitor capacitance its capacitive reactance will change until it equals the inductive reactance of coil which means that the impedance will equal the ohmic resistance only (minimum impedance) and current will be maximum value (it’s used in receiver devices)

8- Resonance Circuit Used in receivers to receive a specific wave

BB. Figures

CC. Deductions 1- Frequency of current in resonant circuit

- In resonant circuit, current will be maximum when inductive reactance equal capacitive reactance - XL= XC

- 2fL = 1 / 2fC- f 2=1/4LC

43

f = 1/2√ LC

Mr. Ahmed Hekal

DD.Factors dependent on : 4- Angle of deviation in Hot-Wire Ammeter - Square of current intensity 5- Inductive reactance of a coil XL= 2 f L

4- Self-induction coefficient 5- Frequency of current

6- Capacitive Reactance of a capacitor XC= 1/ 2 f C1- Capacity of capacitor2- Frequency of current

7- Total impedance Z = √ R2+(XL-XC)2

1- Ohmic Resistance2- Inductive reactance3- Capacitive reactance

8- Frequency of resonant circuit f = 1/2√ LC1- Square root of capacity2- Square root of self-induction coefficient

I. Comparisons Hot-Wire Ammeter Moving Coil Ammeter

Idea Of Work Expansion resulting on thermal effect of electrical current

Torque resulting on the magnetic effect of electrical current

Usage Measuring intensity of DC current and effective value of AC current

Measuring DC current only

Scale (graduation) Non-regular RegularEffect of room temperature

It’s affected by room temperature It doesn’t affected

Pointer move It moves slowly when passing the current or cut-off

It moves faster when passing the current or cut-off the current

44

Mr. Ahmed Hekal

Circuit of R and XL (RL) circuit

Circuit of R and XC

(RC) circuitCircuit of XL, XC,R(RCL) Circuit

Resonant Circuit

Circuit

Total Voltage V = √ VR2+ VL

2 V = √ VR2+ VC

2 V = √ VR2+ (VL- VC)2 VL=VC

V = VR

Impedance Z = √ R2+XL2 Z = √ R2+XC

2 Z = √ R2+(Xl-XC)2 XL= XC

Z = RPhase Angle Tan = VL/VR = XL/XR

is Positive

Tan = - VC/VR

= -XC/XR

is Negative

Tan = (VL-VC) / VR

=(XL-XC)/R

When XL> XC is PositiveWhen XL< XC is Negative

Tan = 0

45

Mr. Ahmed Hekal

J. Important Explanations

1- Disadvantages of Hot-Wire AmmeterA. Its pointer moves slowly until stop at effective value and also it returns back to zero slowlyB. Platinum-Iridium wire is affected by the room temperature which causes some errors in readings

called zero error2- AC circuit contains non-inductive resistance

A. V = Vmax. sin ω tB. I = V / R So I = Imax. sin ω tC. From A. and B. we found that in this circuit voltage and current are in phase it means they reach 0

together and maximum value together

3- AC circuit contains an inductive (non-resistive) coil

A. When closing the circuit, voltage between terminals of coil reaches Vmax. ,current grows gradually and voltage decreases gradually according to the reverse induced e.m.f. until current reaches maximum at the moment in which voltage is zero

B. Induced current is generated in the coil and it resist the change causing it this is the cause of lag1-ging current in reaching maximum with voltage

C. Vinduced = - L /t

46

Mr. Ahmed Hekal

D. Current lags عن voltage by 90o or ¼ cycle يتأخرE. XL = 2πfL

4- AC circuit contains a capacitor

A. In 1st quarter, current reaches maximum, where –ve charges are transferred on plate A and its potential is decreased, these charges affect plate B and repulsed with –ve charges on plate B so plate B has only +ve charges, at this moment capacitor is charged and current stops (equal 0)because voltage on capacitor = voltage of source = maximum value

B. In 2nd quarter e.m.f.source decreases so potential difference across the capacitor is higher than source so it discharges in source, current will reach maximum and voltage of capacitor reaches 0

C. In 3rd quarter, capacitor will charge again but in the opposite direction (plate B is –ve and Plate A is +ve) until its voltage reaches e.m.f.source so current stops =0 and voltage is maximum

D. In 4th quarter, capacitor discharges and its voltage will be 0 and current is maximum I = C V/t

E. Current leads يسبق voltage by 90o or ¼ cycleF. XC= 1 / 2πfC

5- RL CircuitA. In the coil V leads by 90o or ¼ cycleB. In Ohmic resistance V and are in phase C. Current is the same because they are connected in series D. Voltage of coil leads voltage of resistance by 90o

E. V = √ VR2+ VL

2

F. Z = √ R2+XL2

6- RC CircuitA. In capacitor V lags by 90o or ¼ cycleB. In Ohmic resistance V and are in phase C. Current is the same because they are connected in series D. Voltage of resistance leads voltage of capacitor by 90o

E. V = √ VR2+ VC

2

F. Z = √ R2+XC2

7- RCL circuitA. In the coil V leads by 90o or ¼ cycleB. In Ohmic resistance V and are in phase C. In capacitor V lags by 90o or ¼ cycleD. Current is the same because they are connected in series E. V = √ VR

2+ (VL- VC)2

F. Z = √ R2+(Xl-XC)2

47

Mr. Ahmed Hekal

8- Oscillator CircuitA. Structure

I. Inductive coil of a very small resistance II. Capacitor

III. Battery and all are connected in parallelB. Operation

I. When close key “A”- Current passes in the capacitor - One plate (connected to positive pole) is charged with

positive charge, and the other plate is charged with negative charge

- Current stops when potential difference across capacitor is equal to VBattery1

- Energy is stored in capacitor in form of electrical field - Open key “A” ,now capacitor is charged

II. When closing key “B”- Capacitor discharges through coil and current flows from the positive plate to negative plate, potential

difference between plates will decrease until it vanishes and the electrical field disappears - The coil stores energy in form of magnetic field resulting on the current passes through it- In the beginning, the potential difference through capacitor is high so current passing through the coil is

high, after an interval of time P.D. in capacitor decreases and current also decreases in the coil - This shortage in current leads to generate a direct induced e.m.f in the coil by its self-induction, this

induced e.m.f. attracts positive charges from the positive plate to negative plate, so positive plate will be charged with negative charges and negative plate will be charged with positive charges

- Capacitor is now charged in opposite direction and this means that magnetic energy is converted again to electrical energy

- Capacitor will start discharging in opposite direction in the coil and electrical field is converted to a magnetic field and so on , which causes many oscillations in the circuit according to this exchange

9- Relation between frequency and (XL XC R Z)

- Impedance Z decreases until it reaches minimum Z =R when XL=XC and it increases with frequency- Current increases with frequency until it reaches maximum when XL=XC then it decreases with frequency

increase, this is because current is inversely proportional with impedance- Circuit is resonant (in resonance state) when XL=XC

48f = 1/2√ LC

Mr. Ahmed Hekal

G. What Happens in these cases 1- Flow of AC current in an Ohm resistance to its temperature

- Its temperature increases because of energy loss in form of thermal energy2- AC or DC current pass through the Hot-Wire Ammeter

- Thermal energy is generated in the Platinum-Iridium wire so it expands and allows to the silk thread to make the roller to rotate and pointer to deviate so it gives the value of effective current

3- Cutting-off current passes in Hot-Wire Ammeter- The wire is cooled and attracts the silk thread which rotate the roller to returns the pointer to zero

4- The silk thread is cut- The expansion of platinum-iridium wire will not affect the roller or the pointer so, Ammeter will not give

a reading 5- Passage of AC current in an inductive coil to the phase angle between current and voltage

- Voltage leads current by 90O or ¼ cycle6- if frequency of AC current is highly increased

- the inductive reactance will increases also by relation XL= 2 f L until it prevents the flow of current7- Capacitor is connected to DC source

- Current flows in the circuit in a small interval of time then it decreases until it vanished when P.D. of capacitor = VBattery

8- Passage of AC current in a circuit contains capacitor to the phase angle between current and volt- Current leads voltage by 90O or ¼ cycle

9- High Increase of frequency of electrical current passes through a capacitor- Capacitive reactance will decrease according to relation XC= 1/ 2 f C and circuit is considered short-

circuit10- Connecting a resistance with an inductive coil and AC source to the phase angle between current and

total voltage- Voltage leads current by angle where tan = VL / VR = XL / R

11- Connecting a resistance with an inductive coil and AC source to the phase angle between current and total voltage

- Current leads voltage by angle where tan = - VC/ VR = - XC / R12- Connecting a charged capacitor to inductive coil

- Capacitor discharges in the coil and an instantaneous current flows ,so a reverse induced e.m.f. is generated in the coil in opposite direction of the main current, this operation is reversed several times causing oscillations so it’s called Oscillator circuit

13- The inductive reactance equals the capacitive reactance in RCL circuit- The circuit is resonant, and total impedance is minimum (Z =R) and current is maximum , voltage and

current are in phase = 0 and frequency f = 1/2√ LC14- Replacing AC source with DC source of the same effective value in RL circuit to the current intensity

- Current will increase because total impedance is decreased when AC source is replaced by DC source

- In case of AC : current has frequency f and coil has inductive reactance XL= 2fL so Z is high Z = √ R2+XL2

- In case of DC : frequency =0 and XL=0 so Z is low Z = R only , current will increase

49

Mr. Ahmed Hekal

K.Give reason 31- Hot-Wire Ammeter is used to measure AC and DC currents

- As it generally depends on the thermal effect of any electrical current, it measures the effective value of current according to the expansion of Iridium-Platinum wire by heat caused by current passage in the wire.

32- An alloy of Platinum-Iridium used in the Hot-Wire Ammeter- As it expands easily by heat when current flows through it

33- Platinum-Iridium wire is connected in parallel with a resistance R- To work as a shunt resistance (it divides the current) to allow a suitable part of current to pass through

the wire 34- Hot-Wire Ammeter is connected in series in the electrical circuit

- To measure the current needed to be measured not part of it35- Hot-Wire Ammeter divisions are not regular

- Because the quantity of heat generated in the wire is directly proportional with the square of effective current not the current only

36- There is an error in Hot-Wire Ammeter called zero error- Because the platinum-iridium wire is affected by the room temperature

37- The platinum-iridium wire is tensed on a board made of a material has the same expansion coefficient of the wire and insulated from it- To overcome the error caused by affecting the wire by the room temperature

38- Current and Volt are in phase in ohmic resistance circuit- Because V = Vmax sin t and = V / R , = (Vmax sin t) / R So = max sin tThey have the same phase angle so they vanishes together and reaches maximum together

39- At very high frequencies AC current may not pass through the inductive coil- Because inductive reactance is very high XL= 2 f L and circuit is considered open circuit

40- Passage of AC in an inductive coil (non-resistive) don’t loss energy - Because the only existent resistance is the inductive reactance that results in generating reversed

induced e.m.f in the coil so it maintains the energy in form of magnetic field41- When increasing number of turns for a coil the inductive reactance increases if AC current of a constant

frequency passes- Because inductive reactance XL is directly proportional with self-induction coefficient L when the

frequency is constant XL= 2 f L And self- induction is directly proportional with square of number of turns L = µ N2 A / L (length)

42- Inductive reactance increases when put wrought iron core inside the coil and passing the same AC current- Because inductive reactance XL is directly proportional with self-induction coefficient L when the

frequency is constant XL= 2 f L - And self- induction is directly proportional with permeability coefficient L = µ N2 A / L (length) - And permeability coefficient of wrought iron is higher than Air

43- When connecting group of inductive coils in parallel, the resultant inductive reactance is lower than the smallest one

50

Mr. Ahmed Hekal

- Because the reciprocal of the resultant inductive reactance is equal to the sum of the reciprocal of all of them (1/XL = 1/XL1+1/XL2 +1/XL3 +…….)

44- When connecting a capacitor with DC source, current flows in a short time then it vanishes - Current passes from battery to capacitor and +ve charges are placed on one plate and negative charges

placed on the other plate so a reverse potential difference is generated on the capacitor and increases with time and current decreases until Vcapacitor = VBattery , at this moment current stops because there is no difference in potential between battery and capacitor

45- The capacitive reactance doesn’t cause loss in energy

- Because capacitor store electrical energy in form of electrical field46- When an AC current of high frequency passes through a capacitor, the circuit is considered closed circuit

- Because XC= 1/ 2 f C , this means that the capacitive reactance is inversely proportional with frequency so at high frequency the capacitive reactance is very low and current passes in a closed circuit(no resistance)

47- When connecting a group of capacitors in parallel the capacitive reactance for the group is less than the lowest capacitive reactance for each capacitor

Because the total capacitance of a group connected in parallel equals the summation of them (CT = C1 + C2+ C3+ ….) so it will be higher than any of them, and the capacitive reactance is inversely proportional with the capacitance XC= 1/ 2 f C

48- The inductive reactance of a coil passes through it a dc current equals 0- Because DC current is unified in magnitude and direction so its frequency equals 0 and inductive

reactance XL= 2 f L so it will be XL= 049- It’s impossible to produce an inductive coil of resistance zero

- Because any coil made of conducting wires which should have a little value of resistance according to its resistivity

50- If an inductive coil has ohmic resistance is connected to AC source, the total voltage leads current by angle where 0 < < 90 - Because current and volt are in phase in the ohmc resistance and volt leads current by angle of 900 in

the coil so the total voltage leads current by angle tan = VL / VR

51- If a capacitor is connected to an ohmic resistance and AC source of high frequency in series, the current will lead the total voltage by angle where 0 < < 90 - Because voltage and current are in phase in the resistance and current leads voltage by angle of 900 in

the capacitor so the current will lead the total voltage by angle where tan = - VC / VR

52- In Oscillator circuit, the process of charging/discharging stops after an interval of time- Because a part of electrical energy is converted gradually to thermal energy consumed in wires

according to its resistance so after time , AC current decreases and P.D. across capacitor also decreases until it vanishes

53- To continue in charging/discharging process we should feed the capacitor with additional charges after intervals of time - To overcome energy loss as heat according to wires resistance

54- Ohmic resistance has a constant value regardless the value of frequency but inductive reactance and capacitive reactance changes with frequency

51

Mr. Ahmed Hekal

- Because ohmic resistance doesn’t depend on the frequency but inductive reactance and capacitive reactance depend on frequency according to these relations

- XC= 1/ 2 f C- XL= 2 f L -

55- Capacitor allows the AC current to pass through its circuit- When AC current passes, the capacitor is charged in the 1st quarter until voltage of it is equal to VSource

then e.m.f of source decreases in the 2nd quarter so VCapacitor > VSource so capacitor will discharge in the source but source continue in decreasing its e.m.f until it reaches zero at the moment in which VSource

also reached zero and this process is repeated in the 3rd and 4th quarter but in the opposite direction56- In resonance state current intensity is maximum

ORIn resonance state the current and total voltage are in phase - Because the inductive reactance is equal to capacitive reactance so the total impedance Z = R so the

current is maximum value because resistance is minimum value and the voltage and current are in same phase according to these relations

- V = Vmax sin t and = V / R , = (Vmax sin t) / R So = max sin t

57- The average of electrical power consumed in a complete cycle of AC current in an inductive coil is 0- Because coil stores energy in the 1st quarter in form of magnetic field and discharges it in the 2nd quarter

and repeats this in the second half(3rd and 4th quarters ) so after 1 cycle the total power =058- The average of electrical power consumed in a complete cycle of AC current in a resistance is not 0

- Because current needs work to transfer charges in both directions and this work doesn’t depend on the direction of the current

59- We don’t sum the voltages in RCL circuit to get the total voltage- Because each volt has a specific direction so we deals with them as vectors - V = √ VR

2+ (VL- VC)2

60- When replacing DC voltage source by an AC voltage source of the same effective e.m.f. in RL circuit, the impedance increases - Because an inductive reactance is generated in the coil according to its self-induction which wasn’t exist

in case of DC because frequency was zero ,- It was Z = R and became Z = √ R2+XL

2

52

Mr. Ahmed Hekal

AC and DC current Comparison

Hot Wire Ammeter

Used to measure the effective value of AC

Construction:

1- Thin wire of (platinum-Iridium) alloy, this wire is stretched between terminals of the device, so when it heated up it will expand

2- One end of silk thread attached to the middle of the wire, the other end rolled over a roller which is fixed on a spring to the wall

3- A pointer is attached to roller and moves over a scale4- The alloyed wire is connected with a shunt resistance in parallel

53

Direct Current DC

1- It’s a constant value current that flows from +ve pole to –ve pole of a battery (conventional direction)

2- Its sources are (cells, batteries and DC generators)

3- Its e.m.f cannot be raised or reduced

4- Measured by moving coil Galvanometer or Ammeter

5- Used in electrolysis, electroplating and Batteries charging

6- Transferred, but with a big loss of energy

Alternative Current AC

1- It’s a current that changes its value from zero to maximum each quarter cycle and changes its direction each half cycle

2- Its source is AC generators

3- Its e.m.f increases and decreases using transformers

4- Measured by the Hot wire Ammeter which measures its effective value

5- Used in most electrical devices and lightening

6- Transferred with minimal loss of energy

Mr. Ahmed Hekal

Operation of Hot-Wire Ammeter:

1- It’s connected in series 2- When AC passes through the wire, temperature increases and wire will expand3- The silk thread pulls the roller, so pointer will move on the scale 4- Pointer deflection is directly proportional with the current flow5- When current stops the wire is cooled and roller will pull the pointer to zero

Disadvantages

- Pointer is slow in moving.- It’s affected by the room temperature that may cause errors in readings

To overcome that we stretch the wire on a plate that has the same expanding coefficient of the wire material and insulate it from wire

How to calibrate this device?

- Calibrating means to ensure that it’s working good and it can measure the correct effective value- By comparing its reading with the reading of the moving coil Ammeter by connecting both in series in a dc circuit

with rheostat

Notices

54

Mr. Ahmed Hekal

- The scale is not regular because the thermal amount generated in the wire is directly proportional with I2 , not I

- It can measure both AC and DC currents because the thermal effect of current doesn’t rely on the current direction

55

Mr. Ahmed Hekal

56

LawsCapacitor A. Capacitive reactance

XC= 1 / 2πfC = 1 / CB. Capacity

C = Q / VC. Compare between 2 capacitors capacitive

reactanceXC1/ XC2= f2 C2 / f1 C1 = C 2 / C1

D. AC current intensity in a capacitor

= VC / XC

E. Connecting Capacitorsa- In parallel

1/XC= 1/XC1+1/XC2 +1/XC3 +……

CT =C1+ C2 + C3

In case of capacitors are similar

CT = C1 *n

XC = XC1 / n

b- In series

XC= XC1+ XC2 + XC3 +……

1/CT = 1/C1 + 1/C2 + 1/C3

In case of capacitors are similar

CT = C1 /n

XC = XC1 * n

LawsInductive Coil

A. Inductive reactance XL= 2 f L = L

B. Induction or (self-induction coefficient)L = / L (length)

C. Compare between 2 coils inductive reactance

XL1/ XL2= f1 L1 / f2 L2 = L 1 / L 2

D. AC current intensity in a coil

= VL / XL

E. Connecting inductive Coilsa- In parallel

1/XL = 1/XL1+1/XL2 +1/XL3 +……

1/LT = 1/L1+ 1/L2 + 1/L3

In case of coils are similar

L = L1 / n

XL = XL1 / n

b- In series

XL= XL1+ XL2 + XL3 +……

LT = L1+ L2 + L3

In case of coils are similar

LT = L1 * n

XL = XL1* n