unit 3 day 2: resistivity, power & ac current resistivity and its temperature dependence...
TRANSCRIPT
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