The r.m.s. value of potential difference V sh | vedclass

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(C) Given the potential difference $V$ as a function of time $t$:$V = V_0$ for $0 \leq t \leq \frac{T}{2}$$V = 0$ for $\frac{T}{2} \leq t \leq T$The $

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$\frac{V_0}{\sqrt{2}}$

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(C) Given the potential difference $V$ as a function of time $t$:$V = V_0$ for $0 \leq t \leq \frac{T}{2}$$V = 0$ for $\frac{T}{2} \leq t \leq T$The $r.m.s.$ value is defined as:$V_{rms} = \sqrt{\frac{1}{T} \int_0^T V^2 dt}$Substituting the given values:$V_{rms} = \sqrt{\frac{1}{T} \left( \int_0^{T/2} V_0^2 dt + \int_{T/2}^T 0^2 dt \right)}$$V_{rms} = \sqrt{\frac{1}{T} \left( V_0^2 [t]_0^{T/2} + 0 \right)}$$V_{rms} = \sqrt{\frac{V_0^2}{T} \cdot \frac{T}{2}}$$V_{rms} = \sqrt{\frac{V_0^2}{2}}$$V_{rms} = \frac{V_0}{\sqrt{2}}$

The $r.m.s.$ value of potential difference $V$ shown in the figure is

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