Physics 213General Physics

Lecture 5

2

Last Meeting: Capacitance

Today: Current and Resistance

Energy Stored in a Capacitor

Energy stored = ½ Q ΔV

From the definition of capacitance, this can be rewritten in different forms

C2

QVC

2

1VQ

2

1Energy

22

4

NC

C

CCC

eq

eq

...111

2

21

VCEnergy

NCC

CCC

eq

eq

...

C CC

C

Quiz: The plates of a connected parallel-plate capacitor of capacitance C are brought together to one-third their original separation. The energy stored is now

(a) W/9(b) W/3(c) 3W(d) 9W

Answer: c

221 1,

2 2

QW CV W

C

QUIZ

A fully charged parallel-plate capacitor remains connected to a battery while you slide a dielectric between the plates. Do the following quantities increase, decrease, or stay the same? (a) C; (b) Q; (c) E between the plates; (d) V.

QUIZ

(a) C increases

(b) Q increases

(c) E stays the same

(d) V remains the same

8

9

10

Charge Carrier Motion in a Conductor

The zig-zag black line represents the motion of a charge carrier in a conductorThe net drift speed is small

The sharp changes in direction are due to collisions

The net motion of electrons is opposite the direction of the electric field

Charge Carrier Motion in a Conductor

The drift speed Vd is small (~1meter/hour)

The fermi speed Vf is very fast! Due to quantum mechanics of electrons. (~106 meters/second)

Charge rearrangements and signals travel near speed of light (~108 meters/second)

fv

13

14

15

16

17

18

19

Variety of Resistors

Temperature Variation of Resistivity

For most metals, resistivity increases with increasing temperature

With a higher temperature, the metal’s constituent atoms vibrate with increasing amplitude

The electrons find it more difficult to pass through the atoms

fv

Temperature Variation of Resistivity, contFor most metals, resistivity increases

approximately linearly with temperature over a limited temperature range

ρ is the resistivity at some temperature T

ρo is the resistivity at some reference temperature To To is usually taken to be 20° C

is the temperature coefficient of resistivity

)]TT(1[ oo

22

Energy is turned to heat (random motion)

Electrical Energy and Power

The rate at which the energy is lost is the power

From Ohm’s Law, alternate forms of power are

QV I V

t

22 V

I RR

Electrical Energy and Power, cont2

2 VI R

R

Electrical Energy and Power, final

The SI unit of power is Watt (W)I must be in Amperes, R in ohms and V in

Volts

The unit of energy used by electric companies is the kilowatt-hourThis is defined in terms of the unit of power and

the amount of time it is supplied1 kWh = 3.60 x 106 J