Download rms

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 crosssectional area:
L
  resistivity   m
R
A
Resistivity
• Resistivity is a material property
• The reciprocal of resistivity is conductivity

1

  conductivity   m 
1
• Resistivity is temperature dependent
T  0 1   T  T0  T  resistivit y at temp
0  resistivit y at 20 C
T0  20 C (room temp)
  temp coefficient of resistivit y C

 1
Electric Power
• Electric Power delivered to the
load is:
P
dU dQ

 V
dt
dt
or
P  I  V
or P  I 2 R
2

V 
or P 
R
by substituting V  I  R
V
by substituting I 
R
• SI: Watts (W) 1W = 1 Volt-Amp
Electric Power
• Energy purchased from the power
company to use to power our
home is: P  dt  watt  sec
• We purchase energy in large quantities, so it is
more convenient to use units of:
kw  hr kilowatt  hours 
1kw  hr  1000W  3600s  3.6  10 J
6
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
2
PI R
• Too much current in a wire or a load will cause it
to overheat and may cause fire.
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.
L
R
A
• Use current protection devices
such as fuses or circuit breakers.
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
P
3450W
I

 28.75 A
V
120V
• Extension cords can be a dangerous fire hazard,
if they are rated at 10A or less.
Alternating Current
• DC Current is constant with time.
I0
• AC Current varies periodically with time
I  I 0  sin t   ,   2f
V  V0 sin t   
V V0
I   sin t   
R R
AC Power
P  I 2 R  I 02 R sin( t   ) or
P  P0 sin( t   ) where P0  Peak Power
P  Average Power
• Since the current is squared, power is always
positive
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.
V0
2
2
1
Vrms  V  2 V0 
 .707V0
2
I rms  I 
2
1
2
I0
I 
 .707 I 0
2
2
0
Average Power
P  Vrms  I rms
V0 I 0 V0 I 0 P0




2
2
2 2
2
P  12 I 02 R  I rms
R
or
2
2
V
V
P  12 0  rms
R
R