Ch 18 1

Chapter 18

Electric Currents

© 2002, B.J. Lieb

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 leaving 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:

+ _

9 voltsDevice

Current

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

+

Ch 18 5

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 6

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 7

Example 1

Ch 18 8

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 9

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.

Material 0 ( m) 0 (Co)-1

Silver 1.59 x 10-8 0.0061

Aluminum 2.65 x 10-8 0.00429

Hard Rubber (insulator) 1013 - 1015

Ch 18 10

Example 2

Ch 18 11

Superconductivity

• 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

• 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.

Ch 18 12

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:

VIVt

Q

t

QV

time

energypowerP

and thus:

IVP

Ch 18 13

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.

•The formula for power can be combined with Ohm’s Law to give other versions:

R

VRIIVP

22

Ch 18 14

Example 3

Ch 18 15

Household Power

•Electric companies usually bill by the kilowatt-hour 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 16

Alternating Current

-1.5

-1

-0.5

0

0.5

1

1.5

0 5 10 15

Time

Cur

rent

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

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

ftVV 2sin0

Ch 18 17

Average Power

R

VRIP rms

rms

22

•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

•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:

20II rms

Ch 18 18

Alternating Current in U.S.

-1.5

-1

-0.5

0

0.5

1

1.5

0 5 10 15

Time

Vol

tage

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

Ch 18 19

Example 4

Ch 18 20

Microscopic View of Current

•Read Example 18-13. 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.