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(D) In an alternating current $(AC)$ circuit,the instantaneous voltage is given by $E = E_0 \sin(\omega t)$.The root mean square $(r.m.s.)$ value of a

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$\frac{E_0}{\sqrt{2}}$

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(D) In an alternating current $(AC)$ circuit,the instantaneous voltage is given by $E = E_0 \sin(\omega t)$.The root mean square $(r.m.s.)$ value of an alternating voltage is defined as the square root of the mean of the squares of the instantaneous values over one complete cycle.Mathematically,$E_{rms} = \sqrt{\frac{1}{T} \int_{0}^{T} E^2 dt}$.Substituting $E = E_0 \sin(\omega t)$,we get $E_{rms} = \sqrt{\frac{1}{T} \int_{0}^{T} E_0^2 \sin^2(\omega t) dt}$.Solving this integral,we obtain $E_{rms} = \frac{E_0}{\sqrt{2}}$.

If ${E_0}$ represents the peak value of the voltage in an ac circuit,the r.m.s. value of the voltage will be

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