The instantaneous voltage from an ac source is given by E=300 314… - Vidyadip

Question

The instantaneous voltage from an ac source is given by $\text{E}=300\sin314\text{t};$ what is the rms voltage of the source.

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Answer

Given equation is E $=300\sin314\text{t}$
Comparing with standard equation $\text{E = E}_0\sin\omega\text{t},$ we have
$\text{E}_0=300\text{volt}$
So, $\text{E}_{\text{rms}}=\frac{\text{E}_0}{\sqrt{2}}=\frac{300}{\sqrt{2}}=150\sqrt{2}\text{volt}$
$=150\times1.414=212\text{V}$

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