The mean and rms value of an alternating volt | vedclass

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(A) For the given square wave,the voltage $V(t)$ is $V_0$ for $0 < t < T/2$ and $-V_0$ for $T/2 < t < T$.$1$. Mean value for a half cycle ($0$ to $T/2

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$V_0, V_0$

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(A) For the given square wave,the voltage $V(t)$ is $V_0$ for $0 $1$. Mean value for a half cycle ($0$ to $T/2$):$V_{mean} = \frac{1}{T/2} \int_0^{T/2} V_0 dt = \frac{2}{T} [V_0 t]_0^{T/2} = \frac{2}{T} \cdot V_0 \cdot \frac{T}{2} = V_0$.$2$. $rms$ value for a full cycle (or half cycle):$V_{rms} = \sqrt{\frac{1}{T} \int_0^T V^2 dt} = \sqrt{\frac{1}{T} [\int_0^{T/2} V_0^2 dt + \int_{T/2}^T (-V_0)^2 dt]} = \sqrt{\frac{1}{T} [V_0^2 \cdot \frac{T}{2} + V_0^2 \cdot \frac{T}{2}]} = \sqrt{\frac{1}{T} \cdot V_0^2 \cdot T} = V_0$.Thus,the mean and $rms$ values are $V_0$ and $V_0$ respectively.

The mean and $rms$ value of an alternating voltage for a half cycle,as shown in the figure,are respectively:

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