PHYSICS 1B – Fall 2007

Electricity&

Magnetism

Professor Brian Keating

SERF Building. Room 333

Schedule

• Today: Current, resistance• Wednesday: Resistance and Power• Friday: Circuits with Resistors/Capacitors• Monday 11/12: NO CLASS• Wednesday 11/14: Magnetism Ch 18• Friday 11/16: QUIZ 3 (Ch 17 and 18)

• New Syllabus due to the fires: Posted Soon

17.1 Electric Current

Electric currentDrift speedCurrent sources: Batteries

Quiz results – posted soon

Charge flow slowly in a wire

Carry kinetic energy like water in a pipe

The energy can be released eg. Lightbulb

Iq

q

There is an electric field in the conductor.Non-Equilibrium System. – Charges move

Electric Current, I

+q

qI

t

!=!

I

rate of +charge flow through a surface

Units Coulombs/sec – Ampere (A)

A flashlight bulb carries a current of 0.1 A. (a) Findthe charge passed in 10 s. (b) How many electronsdoes this correspond to?

0.1(10) 1

qI

t

q I t C

!=!

! = ! = =

(a)

(b)18

19

16.2 10

1.6 10

q Ne

qN x electrons

e x !

=

= = =

Drift Velocity

E

e-

Collisions of electron with the lattice (a.k.aresistance) slows down the velocity.

1410 s! "

#

Drift velocity- Average velocity in the direction of the flow.

Current – like a fluid through a pipe.

Rate of flow is

( )arg arg

d

ch e ch e volume A xqn qnAv

time volume time t

!" #" # " #= = =$ %$ % $ %!& '& ' & '

d

qI qnAv

t

!= =!

A

d

xV

t

!=!

Vd –Drift velocity

n – no. of charge carriers/volume

q- charge per charge carrier

17.2 Find the drift velocity of electrons in Cu. For I=10 A,A=3x10-6 m2. Use density of Cu, ρ=8.95 g/cm3(each atomof Cu contributes 1 carrier electron) MA=63.5g/mole

dI qnAv= q e=

6 3

3 3 3

236 6

28 3

10

6.0 10(10 ) 8.95(10 )

63.5

8.5 10 /

A

A

atoms grams cm atomsn

m cm m gram

N xn

M

n x e m

!

= =

= =

=

19 28 6

10

1.6 10 (8.5 10 )(3 10 )

d

d

Iv

enA

vx X X

! !

=

=

I

vd

42.4 10 /

dv x m s

!=

The drift velocity is very low.

The current is large because of the large number of charge carriers.

The electrical signal travels fast, because electrons interact and “push” other electrons in the conductor

Voltage sourcesBatteries

VI Voltmeter

Cu

Zn

e e

Cu++ Zn++

Chemical Energy->ElectricalEnergy

Cu has a higher affinity forelectrons than Zn, producesΔV: Zinc more readily loseselectrons than copper, soplacing zinc and coppermetal in solutions of theirsalts can cause electrons toflow through an external wirewhich leads from the zinc tothe copper.

ions

How much charge is equal to 2100 mAh (milliamp hours)

charge=(current)(time)

3

2.1 1

2.1 3600

7.6 10

Q It Ampx hr

CQ s

s

Q x C

= =

! "= # $

% &

=

Amp hour ( unit of charge)

Ni-MH Nickel metal hydride battery

A battery with a 2 amp hr rating is used to power a flashlight that draws 5 A of current. How long will the battery last

2 .0.4

5

Q I t

Q amp hrt hr

I amp

= !

! = = =

Voltages in series

V

Voltmeter- acts as the load

ΔV2

ΔV1

ΔV= Δ V1+ Δ V2

Ideal voltmeter draws no current

Voltages in parallel

VΔ V Δ V11

Δ V= Δ V1

The current isincreased 2 fold

Resistance

R units Volts/Ampere , Ohms (Ω)

ΔV

I

R

Resistance Chapter 17.4

Resistance

VR

I

!=

I

V2V1 ΔV

Resistance, units Volts/Ampere = Ohm (Ω)

Resistance causes conversion of potential energy to heat.

Resistors

carbon resistorswire wound resistorsthin metal film resistors

Ohm’s Law

I V! "1

I VR

V IR

= !

! =

I

ΔV

Slope=1/R

For many conductors I is linear with ΔV,

R is a constant

Gravitational analogy to ΔV=IRWater flow in a river

Water flow is fast where the slope is steep(large potential drop).

H2O resistor

E&M & H2O

E&M & H2O

InductorsCapacitor

Movies

• Water/Circuit Analogies

Inductor Inductor

Inductor Inductor

Inductor Inductor

Inductor Inductor

Some materials show non-ohmic resistance

Semiconductor diode

ΔV

I

Does the resistance of the diode increase ordecrease as ΔV increases?

I

Resistors

carbon resistorswire wound resistorsthin metal film resistors

Resistivity, ρProperty of conducting material

LR

A!=

AL

! Resistivity, ohms meter (Ω·m)

Resistance of a resistor is determined by the geometry of the resistor and the resistivity.

Voltage – Pressure Analogy

Some materials show non-ohmic resistance

Semiconductor diode

ΔV

I

Does the resistance of the diode increase ordecrease as ΔV increases?

A light bulb connected to a 3.0 V battery draws acurrent of 0.2 A. Find the resistance of the light bulb.

3.013

0.2

V IR

VR

I

=

= = = !

We assume that the resistance of the wires is negligiblecompared to the resistance of the light bulb.

I

ΔVR

Voltages in Parallel

Circuits with Resistors