Chapter 20Chapter 20

Circuit ElementsCircuit Elements

(capacitor, resistor, and Ohm’s (capacitor, resistor, and Ohm’s law)law)

CapacitanceCapacitance

A capacitor is a device used in a A capacitor is a device used in a variety of electric circuitsvariety of electric circuits

The The capacitancecapacitance, C, of a capacitor is , C, of a capacitor is defined as the ratio of the magnitude defined as the ratio of the magnitude of the charge on either conductor of the charge on either conductor (plate) to the magnitude of the (plate) to the magnitude of the potential difference between the potential difference between the conductors (plates)conductors (plates)

CapacitorCapacitor

A

Any two conductors separated by an insulator: capacitor

d

C = oA/do = 8.85x10-12 F/m

Q =CV

[C] = C/V = Farad

C

Parallel-Plate CapacitorParallel-Plate Capacitor

The capacitance of a device depends The capacitance of a device depends on the geometric arrangement of the on the geometric arrangement of the conductorsconductors

For a parallel-plate capacitor whose For a parallel-plate capacitor whose plates are separated by air:plates are separated by air:

d

AC o o = 8.85x10-12 F/m

Parallel connection Series connection

C1

C2

C3

C1C2 C3

Ceq = C1 + C2 + C3

1/Ceq = 1/C1+1/C2+1/C3

Ceq

ExampleExample

Three capacitors CThree capacitors C11=1=1F, CF, C22=2 =2 F, F, CC33=6 =6 F. Find capacitance of the F. Find capacitance of the equivalent capacitor.equivalent capacitor.

Ceq

Applications of Capacitors – Applications of Capacitors – Camera FlashCamera Flash

The flash attachment on a camera The flash attachment on a camera uses a capacitoruses a capacitor• A battery is used to charge the capacitorA battery is used to charge the capacitor• The energy stored in the capacitor is The energy stored in the capacitor is

released when the button is pushed to released when the button is pushed to take a picturetake a picture

• The charge is delivered very quickly, The charge is delivered very quickly, illuminating the subject when more light illuminating the subject when more light is neededis needed

Applications of Capacitors -- Applications of Capacitors -- ComputersComputers

Computers use Computers use capacitors in many capacitors in many waysways• Some keyboards use Some keyboards use

capacitors at the capacitors at the bases of the keysbases of the keys

• When the key is When the key is pressed, the capacitor pressed, the capacitor spacing decreases spacing decreases and the capacitance and the capacitance increasesincreases

• The key is recognized The key is recognized by the change in by the change in capacitancecapacitance

H-ITT remotesH-ITT remotes• You can buy the remotes from most You can buy the remotes from most bookstores. Buy only the H-ITT remotes, no bookstores. Buy only the H-ITT remotes, no Turning point remotes.Turning point remotes.

• Register remotes (if you got an email with Register remotes (if you got an email with the score then you are ok).the score then you are ok).

• Tune remotesTune remotes

• Answer the questions in classAnswer the questions in class

• Look for your registration number on the Look for your registration number on the screen. In subsequent classes your number screen. In subsequent classes your number will appear in the same spot.will appear in the same spot.

• You have 4 attempts.You have 4 attempts.

• Check your email for quiz scoresCheck your email for quiz scores

A capacitor is designed so that one plate is large and the other is small.

If the plates are connected to a battery, (a) the large plate has a

greater charge than the small plate, (b) the large plate has less charge

than the small plate, or (c) the plates have charges equal in

magnitude but opposite in sign.

QUICK QUIZ

QUICK QUIZ ANSWER

(c). The battery moves negative charge from one plate and puts it on the other. The first plate is left with excess positive charge whose

magnitude equals that of the negative charge moved to the

other plate.

Electric CurrentElectric Current

Whenever electric charges of like Whenever electric charges of like signs move, an signs move, an electric currentelectric current is is said to existsaid to exist

The current is the The current is the rate at which the rate at which the charge flows through the wirecharge flows through the wire

The SI unit of current is Ampere (A)The SI unit of current is Ampere (A)• 1 A = 1 C/s1 A = 1 C/s

t

qI

Electric Current, contElectric Current, cont

The direction of current flow is the The direction of current flow is the direction positive charge would flowdirection positive charge would flow• This is known as This is known as conventional current flowconventional current flow

In a common conductor, such as copper, the current In a common conductor, such as copper, the current is due to the motion of the negatively charged is due to the motion of the negatively charged electronselectrons

It is common to refer to a moving charge It is common to refer to a moving charge as a mobile as a mobile charge carriercharge carrier• A charge carrier can be positive or negativeA charge carrier can be positive or negative

Current: amount of charge flowing through a point per unit time

Current flows from higher potential to lower potential

I

= R I

Ohm’s law

R

ExampleExample

In a tv tube, 5 x 10In a tv tube, 5 x 101414 electrons shoot electrons shoot out in 4 s. What is the electric out in 4 s. What is the electric current? current?

ResistanceResistance

In a conductor, the voltage applied In a conductor, the voltage applied across the ends of the conductor is across the ends of the conductor is proportional to the current through proportional to the current through the conductorthe conductor

The constant of proportionality is the The constant of proportionality is the resistanceresistance of the conductor of the conductor

I

VR

Resistance, contResistance, cont

Units of resistance are Units of resistance are ohmsohms ( (Ω)Ω)• 1 1 Ω = 1 V / AΩ = 1 V / A

Resistance in a circuit arises due to Resistance in a circuit arises due to collisions between the electrons collisions between the electrons carrying the current with the fixed carrying the current with the fixed atoms inside the conductoratoms inside the conductor

Ohm’s LawOhm’s Law

Experiments show that for many Experiments show that for many materials, including most metals, the materials, including most metals, the resistance remains constant over a wide resistance remains constant over a wide range of applied voltages or currentsrange of applied voltages or currents

This statement has become known as This statement has become known as Ohm’s LawOhm’s Law• V = I RV = I R

Ohm’s Law is an empirical relationship Ohm’s Law is an empirical relationship that is valid only for certain materialsthat is valid only for certain materials• Materials that obey Ohm’s Law are said to be Materials that obey Ohm’s Law are said to be

ohmicohmic

V = R IResistance, R = V/I[R] = V/A = Ohm

For a fixed potential difference across a resistor,the larger R, the smaller current passing through it.

Req

Parallel connection Series connection

R1

R2

R3

R1R2 R3

Req = R1 + R2 + R3

1/Req = 1/R1+1/R2+1/R3

Q2. What is the ratio of the current Q2. What is the ratio of the current flowing through each resistor (Iflowing through each resistor (I11:I:I22) in ) in the circuit?the circuit?

1.1. 1:11:1

2.2. 3:13:1

3.3. 1:41:4

4.4. Need more info.Need more info.

6 V

R1 = 10

R2 = 30

• Electrical wires can be bent and/or stretched.• A Node point (branching point) can be moved arbitrarily along the wire.

There are n identical resistors connected in parallel. Req?

1/Req = 1/R + 1/R + 1/R + … + 1/R = n/R

Req = R/n

Ra

Rb

(1) 1/Req = 1/Ra + 1/Rb

(2) Req is smaller than Ra and Rb

20

25

Req ≈ 10

1000 = 1k

2

Req < 2Practically all the current flowsThough the bottom one!!

Ohm’s law:Ohm’s law: = R = R·I·I

R1 = 6

6 V

I = /R = (6 V)/(6 Ohm) = 1.0 A

What is the electric potential at ? We cannot tell the absolute potential at this point. If at is +6 V, then 0 V at If at is +3 V, then -3 V at

For both, the potential diff. is 6 V.

To be able to specify absolute potential at a given point, we need to specify a reference point “0” potential.

GROUND

R1 = 6

6 V = “0”

Then, at is +6 V.

R1 = 6

6 V

R2=4 R3=2

= R3I = 2 (V) = R2I = 4 (V)

= 4 + 2 = 6 (V)

= 2 V