Question

The $ rms $ value of potential difference $ V_0 $ shown in figure is

• A. $ V_0 $
• B. $ \frac{V_{0}}{\sqrt{2}} $
• C. $ \frac{V_{0}}{2 } $
• D. $ \frac{V_{0}}{\sqrt{3}} $

Answer 1

Answer: (B)

Given, $V_{rms}^2 = \frac{1}{T} \int\limits_{0}^{T} V^2 dt $
$ = \frac{1}{T} \int\limits_{0}^{\frac{T}{2}}V^2_{0} dt + \frac{1}{T} \int\limits_{\frac{T}{2}}^{T} 0 dt$
$= \frac{V_0^2 }{T} \times \frac{T}{2} = \frac{V_0^2}{2}$
$\therefore $ According to the given figure,
$\therefore V_{rms} = \frac{V_0^2}{\sqrt{2}}$