The average power dissipated in a pure capacitor in an AC circuit is:

Solution

Physics sir · 3 steps

In a pure capacitor the current leads the voltage by exactly 90°, and cos 90° = 0.

1. Average power formula. For any AC circuit the average power is Vᵣₘₛ Iᵣₘₛ cos φ, where φ is the phase difference between voltage and current.

   P_(avg) = Vᵣₘₛ Iᵣₘₛ cos φ

2. Phase in a capacitor. In a pure capacitor the current leads the voltage by φ = 90°, so the power factor is cos 90° = 0. The capacitor stores energy for one quarter cycle and returns all of it to the source in the next quarter cycle.
3. So. P_(avg) = Vᵣₘₛ Iᵣₘₛ × 0 = 0. The average power dissipated is zero, option (c).

The idea to keep. Average power needs the power factor cos φ. Pure L or pure C means φ = 90°, so no power is used on average. Only a resistance dissipates power.

Answer from the NTA final answer key. Solution by PrepWiser.