Question

The $\text{RMS}$ value of potential difference $V$ shown in the figure is

• A. $V_0$
• B. $\frac{V_0}{2}$
• C. $\frac{V_0}{\sqrt{3}}$
• D. $\frac{V_0}{\sqrt{2}}$

Answer 1

The correct option is D $\frac{V_0}{\sqrt{2}}$


$V=V_0$ for $[0\le t\le \frac{T}{2}]$

$V=0$ for $[\frac{T}{2}\le t\le T]$

$V_{rms}={\left[\frac{{\int }_0^T{V}^{2}dt}{{\int }_0^{T}dt}\right]}^{\frac{1}{2}}$


$V_{rms}={\left[\frac{{\int }_0^{T/2}{V}_0^{2}dt+{\int }_{T/2}^T\left(0\right)dt}{{\int }_0^{T}dt}\right]}^{\frac{1}{2}}$

$V_{rms}={[\frac{V_0^2}{T}\times (\frac{T}{2}-0)]}^{\frac{1}{2}}$

$\therefore V_{rms}=\frac{V_0}{\sqrt{2}}$

Hence, option $\left(\text{C}\right)$ is correct.