Question

Prove that the average power taking by a pure capacitor fed with a sinusoidal ac supply in a circuit is zero.

Answer 1

PHASE DIFFERENCE
It is the angle between the voltage and current phasors.
𝜑 = 90°
POWER FACTOR
It is defined as the cosine of the angle between the voltage and current phasors.
Pf = cos𝜑 = cos(90°) = 0
POWER
Instantaneous power P is given by,

𝑝 = 𝑣𝑖
𝑝 = 𝑉_𝑚𝑠𝑖𝑛𝜔𝑡𝐼_𝑚sin (𝜔𝑡 + 90)
𝑝 = 𝑉_𝑚𝐼_𝑚𝑠𝑖𝑛𝜔𝑡𝑐𝑜𝑠𝜔𝑡

𝑝 =`(V_mI_m)/2`𝑠𝑖𝑛2𝜔𝑡
The average power for one complete cycle, P =0
Hence, power consumed by a purely capacitive circuit is zero.