# Prove that the Average Power Taking by a Pure Capacitor Fed with a Sinusoidal Ac Supply in a Circuit is Zero. - Basic Electrical and Electronics Engineering

Sum

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

#### Solution

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 = 𝑉𝑚𝑠𝑖𝑛𝜔𝑡𝐼𝑚sin (𝜔𝑡 + 90)
𝑝 = 𝑉𝑚𝐼𝑚𝑠𝑖𝑛𝜔𝑡𝑐𝑜𝑠𝜔𝑡

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

Concept: Power and Power Factor
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