Question

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

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

Answer 1

Answer: (C)

Voltage is given as $V=V_0$
for $0\ge t\le T/2$
$=0$ for $T/2\ge t\le T$
Rms voltage $V_{rms}=\sqrt{\frac{\underset{0}{\overset{T}{\int }}{V}^{2}dt}{T}}$
Or $V_{rms}=\sqrt{\frac{\underset{0}{\overset{T/2}{\int }}{V}_0^{2}dt}{T}+\frac{\underset{T/2}{\overset{T}{\int }}0dt}{T}}$
Or $V_{rms}=\sqrt{\frac{\underset{0}{\overset{T/2}{\int }}{V}_0^{2}dt}{T}}$
Or $V_{rms}=\sqrt{\frac{V_0^2\times T/2}{T}}$
$\Rightarrow V_{rms}=V_o/\sqrt{2}$