Transcript Power Calculations using rms values resistor ECE 201 Circuit Theory I

Power Calculations using rms values
• Consider a sinusoidal voltage applied to a
resistor
ECE 201 Circuit Theory I
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Determine the average power delivered
1
P
T
1
P
T
t 0 T
 pdt
t0
t 0 T

t0
Vm2 cos 2 (t   v )
R
t 0 T


1 1
P    Vm2 cos 2 (t   v )dt 
R  T t0

1 2
P  Vrms
R
ECE 201 Circuit Theory I
2
If a sinusoidal current is applied
i (t )  I m cos(t   i )
1
P
T
R
P
T
PI
t 0 T
2
2
I
R
cos
(t   i )dt
 m
t0
t 0 T
I
2
m
cos (t   i )dt
2
t0
2
rms
R
ECE 201 Circuit Theory I
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Average Power in terms of rms
Vm I m
P
cos( v   i )
2
Vm I m
P
cos( v   i )
2 2
P  Vrms I rms cos( v   i )
P  Veff I eff cos( v   i )
ECE 201 Circuit Theory I
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Reactive Power in terms of rms
Vm I m
Q
sin(  v   i )
2
Vm I m
Q
sin(  v   i )
2 2
Q  Vrms I rms sin(  v   i )
Q  Veff I eff sin(  v   i )
ECE 201 Circuit Theory I
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