average power ac circuit

Question

Average power in AC circuit P_avg equals?

RankGuru · Accepted Answer

1. **Instantaneous Power**: $p = v \cdot i = (V_0 \sin \omega t) (I_0 \sin (\omega t - \phi))$.
2. **Time Average**: Averaging this over a full cycle:
   - $P_{avg} = \frac{1}{2} V_0 I_0 \cos \phi$.
3. **Using RMS values**: Since $V_{rms} = V_0 / \sqrt{2}$ and $I_{rms} = I_0 / \sqrt{2}$:
   - $P_{avg} = V_{rms} I_{rms} \cos \phi$.
4. **Interpretation**: $\cos \phi$ is the power factor. Power is only consumed by the resistive component of the circuit.

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average power ac circuit

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