Prove that the average power taking by a pure capacitor fed with a sinusoidal ac supply in a circuit is zero.
It is the angle between the voltage and current phasors.
𝜑 = 90°
It is defined as the cosine of the angle between the voltage and current phasors.
Pf = cos𝜑 = cos(90°) = 0
Instantaneous power P is given by,
𝑝 = 𝑣𝑖
𝑝 = 𝑉𝑚𝑠𝑖𝑛𝜔𝑡𝐼𝑚sin (𝜔𝑡 + 90)
𝑝 = 𝑉𝑚𝐼𝑚𝑠𝑖𝑛𝜔𝑡𝑐𝑜𝑠𝜔𝑡
The average power for one complete cycle, P =0
Hence, power consumed by a purely capacitive circuit is zero.