ac rms current

Question

For i = I0 sin ωt, RMS current equals?

RankGuru · Accepted Answer

1. **Definition of RMS**: Root Mean Square ($I_{rms}$) is the effective value of alternating current that produces the same heating effect as a DC current in the same resistance.
2. **Mathematical Definition**: $I_{rms} = \sqrt{	ext{Average of } i^2}$.
3. **Calculation over Cycle**:
   - Average of $\sin^2(\omega t)$ over a full cycle is $1/2$.
   - $I_{rms} = \sqrt{I_0^2 	imes (1/2)} = \frac{I_0}{\sqrt{2}}$.
4. **Numerical Result**: $I_{rms} \approx 0.707 \cdot I_0$.
5. **Standard Usage**: AC ammeters and voltmeters are calibrated to read RMS values.

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