Unit 3 Day 2: Resistivity, Power & AC Current

• Resistivity and its Temperature Dependence

• Electric Power

• Heat Generation in Electric Circuits

• AC Current

• Average power

Resistivity• Resistance R, of a wire is proportional to its

length, and inversely proportional to its cross-sectional area:

A

LR myresistivit

Resistivity• Resistivity is a material property

• The reciprocal of resistivity is conductivity

• Resistivity is temperature dependent

1 1 mtyconductivi

00 1 TTT

10

0

)(20

20

Cyresistivitoftcoefficientemp

temproomCT

Catyresistivit

tempatyresistivitT

Electric Power

• Electric Power delivered to the load is:

or

• SI: Watts (W) 1W = 1 Volt-Amp

Vdt

dQ

dt

dUP

R

VIngsubstitutiby

R

VPor

RIVngsubstitutibyRIPor

VIP

2

2

Electric Power• Energy purchased from the power

company to use to power our home is:

• We purchase energy in large quantities, so it is more convenient to use units of:

sec wattdtP

JsWhrkw

hourskilowatthrkw6106.3360010001

Electric Power• When power is delivered to a load,

the current thru the wires generate heat (thermal energy)

• The power is dissipated in the load as heat because of the resistance of the load

• Too much current in a wire or a load will cause it to overheat and may cause fire.

RIP 2

Preventing Circuit Overheating

• Lower resistance in the wires by using low resistivity material (ie: Cu or Al), use large diameter wires, and keeping wire lengths as short as possible.

• Use current protection devices such as fuses or circuit breakers.

A

LR

Circuit Breakers• Circuit breakers (CB)use a bi-metallic strip to

open the circuit

Household Circuit Management

• Connection of too many household appliances to one circuit will cause a CB to trip

• If this circuit is protected with a 20A CB, it will trip to prevent overheating of the wires and prevent fire

• Extension cords can be a dangerous fire hazard, if they are rated at 10A or less.

AV

W

V

PI 75.28

120

3450

Alternating Current• DC Current is constant with time.

I0

• AC Current varies periodically with time ftII 2,sin0

tR

V

R

VI

tVV

sin

sin

0

0

AC Power

• Since the current is squared, power is always positive

PowerPeakPwheretPP

ortRIRIP

00

20

2

)sin(

)sin(

PowerAverageP

RMS Values• It is difficult to measure peak or average AC

Voltage & Current. Therefore a convenient unit of measure was developed called the rms values.

• rms is an abbreviation for root-mean-square value

• To find the rms value, take the square root of mean value of the squared term.

002

0212 707.

2V

VVVVrms

002

0212 707.

2I

IIIIrms

Average Power

222200000 PIVIV

IVP rmsrms

R

V

R

VP

or

RIRIP

rms

rms

220

21

2202

1