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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.

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Solution

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

𝑝 = 𝑣𝑖
𝑝 = π‘‰π‘šπ‘ π‘–π‘›πœ”π‘‘πΌπ‘šsin (πœ”π‘‘ + 90)
𝑝 = π‘‰π‘šπΌπ‘šπ‘ π‘–π‘›πœ”π‘‘π‘π‘œπ‘ πœ”π‘‘

𝑝 =`(V_mI_m)/2`𝑠𝑖𝑛2πœ”π‘‘
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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