Ch 18 1

Chapter 18

© 2006, B.J. LiebSome figures electronically reproduced by

permission of Pearson Education, Inc., Upper Saddle River, New Jersey Giancoli, PHYSICS,6/E

© 2004.

Ch 18 2

Simple Electric Cell

Sulfuric acid

Zn+ Zn+

Zn+ Zn+

+++

___

Carbon Electrode

(+)

Zn Electrode(-)

•Two dissimilar metals or carbon rods in acid

•Zn+ ions enter acid leaving terminal negative

•Electrons leave carbon making it positive

•Terminals connected to external circuit

•‘Battery’ referred to several cells originally

Ch 18 3

Electric Current

•If we connect a wire between the two terminals electrons will flow out of the negative terminal and toward the positive terminal we have an electric current.•Electric current I is defined as the net amount of charge that flows past a given point per unit time.

t

QI

1 C/s = 1A (ampere)An ampere is a large current and often currents are mA (10-3 A) or A (10-6 A).

Ch 18 4

Electric Circuit• It is necessary to have a complete circuit in order for

current to flow.

• The symbol for a battery in a circuit diagram is:

+ _

Device

+

Ch 18 5

“Conventional” current direction is opposite to actual electron flow direction which is – to +.

Ch 18 6

Ohm’ Law

• For wires and other circuit devices, the current is proportional to the voltage applied to its ends:

I V• The current also depends on the amount of resistance that the wire offers to the electrons for a given voltage V. We define a quantity called resistance R such that

V = I R (Ohm’s Law)• The unit of resistance is the ohm which is represented by the Greek capital omega ().• Thus

A

V1

Ch 18 7

Resistors• A resistor is a circuit device that has a fixed resistance.

Resistor

Circuit symbol

Resistors obey Ohm’s law but not all circuit devices do.

I

V0

I

V0

Resistor non-ohmic device

Ch 18 8

Example 18-1A. A person experiences a mild shock if a current of 80 A flows along a path between the thumb and the index finger. The resistance of this path is 4.0x105 when the skin is dry and 2000 when the skin is wet. Calculate the minimum voltage difference between these two points that will produce a mild shock.

RIV

V

AVDRY

32

100.41080 56

V

AVWET

16.0

100.21080 36

Ch 18 9

Example 18-1B. Calculate the number of electrons per second that flow past a point on the skin in problem 18-1A.

t

QI

sec100.5 14 electrons

electroncharge

sec

#

tQelectrons

C

electron

t

Q19106.1

1

C

electrons

C19

6

106.1

11080

Ch 18 10

Resistivity• In most electronic circuits we ignore the resistance of the wires

because it is small in comparison to the other circuit components• If we need to calculate the resistance of a given wire we can use

its resistivity () which is defined by:

A

LR

where L is the length of the wire and A is the cross sectional area.

A

L

Ch 18 11

Resistivity and Temperature

Ch 18 12

Resistivity and Temperature

)( 00 1 TTT

•Resistivity usually depends on temperature. For most metals the resistivity increases with temperature.•Often the flow of current through a wire is the cause of the temperature change.

where T0 is usually 20o and 0 is the resistivity at that temperature.

Ch 18 13

Example 18-2A A 35.0-m length of cooper wire has a radius of 0.25mm. Calculate the current in the wire if a potential difference of 9.0 V is applied across the length if the wire when the temperature is 20˚C.

[for cooper ρ = 1.68×10-8 Ωm and α = 0.0068 (˚C)-1]

23

8

1025.0

0.351068.1

m

mmR

A

LR

2r

L

0.3

RIV

R

VI A0.3

0.3

0.9 V

Ch 18 14

Example 18-2(B) If the wire in Example 18-2A is heated to 30˚C, what is the resulting current if the voltage difference is 9.0 V?

CCCR 20300068.010.31

30

Since R α ρ, we can see that:

Gives:

00 1 TTT

00 1 TTRRT

A8.2

2.330

R

2.3

0.9 V

30

30 R

VI

Ch 18 15

Superconductivity

• Materials require liquid helium for cooling.

• Since 1987 a new class of “high TC” materials have been discovered that are superconducting up to 160 K.

• Would be many practical applications if some of the difficulties can be overcome.

•The resistivity of certain metals and compounds becomes zero at low temperatures near absolute zero- this state is called superconducting.•Occurs only below a critical temperature TC which is usually close to absolute zero

Ch 18 16

Power in Electric Circuits• Electrical circuits can transmit and consume energy.

• When a charge Q moves through a potential difference V, the energy transferred is QV.

• Power is energy/time and thus:

VI

and thus:

IVP

time

energypowerP

t

QV V

t

Q

Ch 18 17

Notes on Power

wattWs

J

C

J

s

CVIP

•The formula for power applies to devices that provide power such as a battery as well as to devices that consume or dissipate power such as resistors, light bulbs and electric motors.

•For ohmic devices, the formula for power can be combined with Ohm’s Law to give other versions:

RIRIIVIP 2)(

R

VV

R

VVIP

2

Ch 18 18

Household Power•Electric companies usually bill by the kilowatt-hour (kWh.) which is the energy consumed by using 1.0 kW for one hour.

•Thus a 100 W light bulb could burn for 10 hours and consume 1.0 kWh.

•Electric circuits in a building are protected by a fuse or circuit breaker which shuts down the electricity in the circuit if the current exceeds a certain value. This prevents the wires from heating up when carrying too much current.

Ch 18 19

Connection of

Household Appliances

Ch 18 20

Example 18-3 (A) A person turns on a 1500 W electric heater, a 100 W hair dryer and then a 300 W stereo. All of these devices are connected to a single 120 V household circuit that is connected to a 20 A circuit breaker. At what point will the circuit breaker trip off?

dryerwithtrips

breakerCircuit

VIP

AV

WI

dryer3.8

120

1000

AV

WI

bulb83.0

120

100

AV

WI

heater5.12

120

1500

V

PI

AV

WI

stereo5.2

120

300

Ch 18 21

Example 18-3 (B) If electricity costs $0.12 per kWh., calculate the cost of operating all the appliances in the above problem for 2.0 hours.

36.0$

12.0$25.1cos

kWhhkWtHeater

70.0$

072.0$Stereo

24.0$Dryer

024.0$Bulb

Ch 18 22

Alternating Current

•Electrical power is distributed using alternating current (ac) in which the current reverses direction with a frequency of 60 Hz (in the USA).

Ch 18 23

Alternating Current

The current and voltage varies as a sine function as shown above. Thus

ftVV 2sin0

Ch 18 24

Average Power

•Even though the electron motion in ac circuits is back and forth they can still deliver power.

•Because the current and voltage change greatly over a cycle, we have to average over a cycle to get an accurate value for the average power consumed in the circuit

Ch 18 25

Average Power

R

VRIP rms

rms

22

The correct way to calculate this average is to use calculus to average the square of the current over a cycle and then take the square root of the result. This is called a root-mean-square (rms) average:

20I

I rms

Ch 18 26

Alternating Current/Voltage in U.S.

ftVV 2sin0

•In the U.S.: f = 60 Hz V0 170 V Vrms 120 V •In Europe: f = 50 Hz V0 310 V Vrms 220 V

ftII 2sin0

Ch 18 27

Example 18-4 (A) A heater coil connected to a 240-V ac line has a resistance of 34 Ω. What is the average power used?

(B) What are the maximum and minimum values of the instantaneous power?

R

VVIP rms

rmsrms

2

kW

VP 7.1

34

240 2

20

II

rms

rmsVV 2

0

rmsII 2

0

P)2(rmsrms

VI)2(rmsrms

VI 22000

VIP

kW4.3)7.1()2( kW

Ch 18 28

Microscopic View of Current•Read Example 18-14. It studies a 5.0A current in a copper wire that is 3.2 mm in diameter. It finds that the average “free” electron moves with a velocity of 4.7 x 10-5 m/s in the direction of the current. This is called the drift velocity.

•It also assumes the “free” electrons behave like an ideal gas and calculates that the thermal velocity of the average electron is 1.2 x 105 m/s.

•Thus in a wire carrying a current, the electron motion is largely random with a slight tendency to move in the direction of the current. Thus if you could see electrons in a wire carrying current they would appear to be moving randomly.

Ch 18 29

Summary of Units