Question

The voltage time $(V-t)$ graph for triangular wave having peak value $V_0$ is as shown in the figure. The rms value of $V$ in time interval from $t=0$ to $T/4$ is $\frac{V_0}{\sqrt{n}}$. Find $n$.

Answer 1

Answer: 3

$V_{\text{rms }}=\sqrt{\frac{\underset{0}{\overset{T/4}{\int }}{V}^{2}dt}{T/4}}$
$\because V=\frac{V_0}{T/4}t$
$\therefore V_{\text{rms }}=\sqrt{\frac{\underset{0}{\overset{T/4}{\int }}\frac{16V_0^2}{T^2}{t}^{2}dt}{T/4}}=\sqrt{\frac{V_0^2}{3}}$
$V_{\text{rms}}=\frac{V_0}{\sqrt{3}}$