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

$V_{ \text{rms }}=\sqrt{\frac{\int\limits_{0}^{T / 4} V^{2} d t}{T / 4}}$
$\because V=\frac{V_{0}}{T / 4} t$
$\therefore V_{ \text{rms }}=\sqrt{\frac{\int\limits_{0}^{T / 4} \frac{16 V_{0}^{2}}{T^{2}} t^{2} d t}{T / 4}}=\sqrt{\frac{V_{0}^{2}}{3}}$
$V_{ \text{rms} }=\frac{V_{0}}{\sqrt{3}}$