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electric force, charges, capacitors, resistors, series and parallel connection
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Electricity Basic electrical instruments and symbols;
Electric charge and electric field; EP; Capacitance; Current, Resistance, and
EMF; Circuits
Electric charge and Electric field
Field Type Caused By
gravity mass
electric charge
magnetic moving charge
Electric charge and Electric field
Charge is not created or destroyed, it is only transferred.
Conductors and Insulators
transfers charge on contact
does not transfer
charge on contact
Objects usually have equal numbers of positive and negative ? , but it isn't too hard to temporarily create an imbalance. Have you ever received a ? after walking across a carpet? As your feet shuffle across the carpet, they pick up extra ? . Those electrons can't wait for you to touch a ?. As soon as your hand is close, they jump off with a shock and a spark of ? .
Charging Processes
By contactPolarizationInduction
Coulomb’s law
The magnitude of the electric force between two point charges is
directly proportional to the product of the charges and inversely proportional to the square of the
distance between them
Coulomb’s law
Fα q1q2 Fα 1/r2
F= k [q1q2/r2]k=9.0x109Nm2/C2
Example
• Two point charges, q1= +25nC and q2= -75nC, are separated by a distance of 3.0cm. Find the magnitude and direction of a) the electric force that q1 exerts on q2 b) and the electric force that q2 exerts on q1.
• 0.019N towards each other
Electric Field, Electric Forces, and Electric field lines
• Michael Faraday, in the 1830’s, came up with the idea of an Electric Field
• Electric field is the force per unit charge
Electric Field, Electric Forces, and Electric field lines
• Electric field of a point charge is:
E= F/q0
• The E at r is:E=kq1/r2
Example
• What is the magnitude of the electric field at a point 2.0m from a point charge q=4.0nC. (The point charge could represent any small charged object with this value of q, provided the dimensions of the object are much less than the distance from the object to the field point)
• 9.0N/C
Electric Field, Electric Forces, and Electric field lines
Like charges(++) Opposite charges(+-)
Electric Field, Electric Forces, and Electric field lines
E-field lines begin on +
charges and end on -
charges(or infinity).
They enter or leave charge symmetrically.
The number of lines entering or leaving a
charge is proportional to
the charge
The density of lines indicates the strength of E at that point.
No two field lines can cross.
Electric Potential Energy
In a uniform field In a uniform field
+ + + + + + + + + + + + + + + + +
- - - - - - - - - - - - - - - - - - - - - - - - -
+
+
a
b
+ + + + + + + + + + + + + + + + +
- - - - - - - - - - - - - - - - - - - - - - - - -
+
+
b
a
Electric Potential Energy
In a uniform field
• Wa-b=Fd=q0Ed
• U=q0Ey• Wa-b=-ΔU=-(Ub-Ua)
• -ΔU=-q0E(yb-ya)
In a uniform field
• If ya > yb, q0 moves in the same direction as E; field does a pos. Work, U decreases
• If ya < yb, q0 moves in the opp. direction as E; field does a neg. Work, U increases
Electric Potential Energy
Two point charges
• U=[k(qq0)]/r
• U= (1/4πε0)(qq0/r)
Two point charges
a+
b
+
+
rra
rb
q0
Electric Potential
Potential energy per unit charge
V=U/q0
1V=1volt=1J/C
Electric Potential
Due to a point charge
• V= U/q0
• V=(1/4πε0)(q/r)
Collection of point charges
• V= U/q0
• V=(1/4πε0)Σ(qI/rI)
Electric Potential= Work/charge Wab/q0= -ΔU/q0=-(Ub-Ua)/q0=-(Vb-Va)= Va-Vb
Example
• How much work is required to move a charge of 4 nC from a point 2m away to a point 0.5 m away from a point charge of 60 nC? What is the potential difference between these points?
• 3.24x10-6J; Vb-a=810 V
Capacitors and Capacitance
any 2 conductors separated
by an insulator
Stores electric
potential energy
Stores charge
Capacitors and Capacitance
Doubling the magnitude of
Q
Doubles the
electric field
Doubles Potential
difference
Capacitors and Capacitance
The ratio of charge to Potential
difference
Capacitance:1F=farad=1C/V C=Q/Vab
Capacitors and Capacitance in vacuum
Simplest capacitor consists of 2 parallel plates w/area A and
dist. d
When the plates are charged, E is almost
completely localized in the region between the plates
E between the plates is uniform and distributed
over their opposing surfaces
Thus it is a parallel plate capacitor
Capacitors and Capacitance in vacuum
For parallel-plate capacitor in vacuum C= Q/Vab = ε0(A/d)
ε0Permittivity of space
constant= 8.85x10-12F/m
Capacitors and Capacitance
In Series1/Ceq= 1/C1+1/C2+1/C3..
The reciprocal of the equivalent capacitance of a series combination equals the sum of the reciprocals of the individual capacitances.
In Parallel Ceq= C1+C2+C3..
The equivalent capacitance of a parallel combination equals the sum of the individual capacitances.
Capacitors and Capacitance
In Series1/Ceq= 1/C1+1/C2+1/C3..
Q=Q1=Q2=Q3
V1= Q/C1
V2= Q/C2
V= V1+V2+V3+..
In Parallel Ceq= C1+C2+C3..
V=V1=V2=V3
Q1= VC1
Q2= VC2
Q= Q1+Q2+Q3+..
Example
• A parallel-plate capacitor has a capacitance of 1.0F. If the plates are 1.0mm apart, what is the area of the plates?
• 1.1x108m2
Example
• Let C1=6.0μF, C2= 3.0 μF, and Vab= 18V. Find the equivalent capacitance, and find the charge and potential difference for each capacitor when the two capacitors are connected a) in series; b) in parallel
Series: Ceq=2.0 μF; Q= 36 μC; Vac=6.0V, Vcb= 12VParallel: Ceq=9.0 μF; Q1= 108μC, Q2= 54 μC; V= 18V
Atoms, the basic building blocks of ?, are made of three basic components: protons, neutrons and ?. The protons and neutrons cluster together to form the ?, which is the ? part of the atom, and the ? orbit about the nucleus. Protons and electrons each carry a ? . Protons carry a ? charge while electrons carry a ? charge. Neutrons are ? - they carry no charge at all.
Current, Resistance, and EMF
CurrentIs any motion of charge from one region to
another
I=dQ/dt=nqvdA
General expression for current
J=I/A=nqvd
Vector current density
Current, Resistance, and EMF
Resistivity
Ratio of the magnitudes
of E and J
ρ=E/JJ is nearly directly prop. to E: Ohm’s
law
Current, Resistance, and EMF
Resistivity and
temperatureρ(T)=ρ0[1+α(T-T0)]
ρ0 is resistivity at T0; α is the temp. coefficient of
resistivity
Current, Resistance, and EMF
ResistivityRatio of the
magnitudes of E and J
R=ρL/A (relationship between R and
ρ)
ResistanceRatio of V to I for a
particular conductor
(Ohm)R=V/I
Current, Resistance, and EMF
The influence that makes current flow
from lower to higher potential
Electromotive force or emf (E)
(1V=1J/C)
V=E=IR
Current, Resistance, and EMF
Series
• It=I1=I2=I3
• Vt=V1+V2+V3+…
• Rt=R1+R2+R3+…
Parallel• It=I1+I2+I3
• Vt=V1=V2=V3
• 1/Rt=1/R1+1/R2+1/R3
Resistors in Series and Parallel
Junction/ node/ branch
point
A point in a circuit where 3 or more conductors
meet
loopIs any closed conducting path
Resistors in Series and Parallel
• Kirchhoff’s junction rule:– The algebraic sum of the currents into any
junction is zero. (ƩI=0)• Kirchhoff’s loop rule:
– The algebraic sum of the potential differences in any loop, including those associated with emf’s and those of resistive elements, must equal zero. ( V=0)Ʃ
Example
The circuit contains 2
batteries, each with an emf and
an internal resistance, and 2
resistors. Find the current into
the circuit.I=0.5A
Electric Power
Energy consumption
Electric power
• It is the amount of electrical energy one uses up per second
• SI unit is Watt• 1hp= 746 Watts
Examples
• A horse pulled a load with a force of 200N through a distance of 100m in 20 seconds. What is the power of the horse?
Ans. 1000W• A man lifted a load of 80kg to a height of
1.5m in 3 seconds. What is the power in watts?
Ans. 392W
Energy cost
Example
• A 1.5hp air-conditioning unit is used for 10h. How much electrical energy (work) did it consume?
• 11.19kWh• 5.50/kWh• Cost= 65.45Php