Transcript Power Calculations   

Power Calculations
Vm I m
P
cos( v   i )
2
Vm I m
Q
sin(  v   i )
2
S  P  jQ
Vm I m
Vm I m
S
cos( v   i )  j
sin(  v   i )
2
2
Vm I m
cos( v   i )  j sin(  v   i )
S
2
Vm I m j ( v  i )
S
e
2
1
S  Vm I m ( v   i )  Veff I eff ( v   i )
2
ECE 201 Circuit Theory I
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Power Calculations (continued)
S  Veff I eff ( v   i )


S  Veff  v I eff    i
S  Veff e
j v
S  V eff I
I eff e

 j i
*
eff
ECE 201 Circuit Theory I
Complex Conjugate of Ieff
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Summary
*
eff
S  V eff I
1 *
S  VI
2
ECE 201 Circuit Theory I
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Example
v(t )  100 cos(t  15)V
i (t )  4 sin( t  15) A  4 cos(t  105) A
ECE 201 Circuit Theory I
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v(t )  100 cos(t  15)V
i (t )  4 sin( t  15) A  4 cos(t  90  15)
V  10015
*
I  4  105  I  4105
1
S  (10015)( 4  105)
2
S  200120
S  200 cos(120)  j 200 sin( 120)
S  200(0.5)  j 200(0.866)
S  100  j173.2VA
ECE 201 Circuit Theory I
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S  100  j173.21VA
P  100W
Delivering Power
Q  173.21VARS
Absorbing Magnetization
ECE 201 Circuit Theory I
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