ac voltage expression

Question

Instantaneous AC voltage form V = V0 sin(ω t) has rms value:

RankGuru · Accepted Answer

The **rms (root mean square)** value is the effective value of AC that produces the same average heating effect as a DC voltage of that value. 
For a sinusoidal wave $V(t) = V_0 \sin(\omega t)$:
$V_{rms} = \sqrt{\frac{1}{T} \int_0^T V(t)^2 \, dt}$
$V_{rms} = \frac{V_0}{\sqrt{2}} \approx 0.707 V_0$.
Standard household voltage (e.g., $230 	ext{ V}$) is given as the rms value.

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ac voltage expression

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