Question

The voltage time $(V-t)$ graph for triangular wave having peak value $V_{0}$ is as shown in figure.

The rms value of $V$ in time interval from $t=0$ to $T / 4$ is

• A. $\frac{V_{0}}{\sqrt{3}}$
• B. $\frac{V_{0}}{2}$
• C. $\frac{V_{0}}{\sqrt{2}}$
• D. None of these

Answer 1

Answer: (A)

$ V=\frac{V_{0}}{T / 4} t ; V =\frac{4 V_{0}}{T} t $
$ V_{ rms } =\sqrt{\left\langle V^{2}\right\rangle}=\frac{4 V_{0}}{T} \sqrt{\langle t\rangle}$
$=\frac{4 V_{0}}{T}\left\{\frac{\int\limits_{0}^{T / 4} t^{2} d t}{\int\limits_{0}^{1 / 4} d t}\right\}=\frac{V_{0}}{\sqrt{3}}$