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Question
Prove that the average power taking by a pure capacitor fed with a sinusoidal ac supply in a circuit is zero.
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Solution
PHASE DIFFERENCE
It is the angle between the voltage and current phasors.
๐ = 90°
POWER FACTOR
It is defined as the cosine of the angle between the voltage and current phasors.
Pf = cos๐ = cos(90°) = 0
POWER
Instantaneous power P is given by,
๐ = ๐ฃ๐
๐ = ๐๐๐ ๐๐๐๐ก๐ผ๐sin (๐๐ก + 90)
๐ = ๐๐๐ผ๐๐ ๐๐๐๐ก๐๐๐ ๐๐ก
๐ =`(V_mI_m)/2`๐ ๐๐2๐๐ก
The average power for one complete cycle, P =0
Hence, power consumed by a purely capacitive circuit is zero.
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