The rms value of the potential difference v s | vedclass

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(D) The root mean square (rms) value of a periodic function $v(t)$ is defined as $V_{rms} = \sqrt{\frac{1}{T} \int_{0}^{T} v^2(t) dt}$.From the given

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$\frac{v_{0}}{\sqrt{2}}$

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(D) The root mean square (rms) value of a periodic function $v(t)$ is defined as $V_{rms} = \sqrt{\frac{1}{T} \int_{0}^{T} v^2(t) dt}$.From the given figure,the potential difference $v(t)$ is $V_0$ for the interval $0 \le t Thus,$V_{rms}^2 = \frac{1}{T} \left[ \int_{0}^{T/2} V_0^2 dt + \int_{T/2}^{T} 0^2 dt \right]$.$V_{rms}^2 = \frac{1}{T} \left[ V_0^2 \cdot \frac{T}{2} + 0 \right] = \frac{V_0^2}{2}$.Taking the square root on both sides,we get $V_{rms} = \frac{V_0}{\sqrt{2}}$.

The rms value of the potential difference $v$ shown in the figure is

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