Question

A voltage waveform is as shown in the figure. Calculate te ratio of $\text{rms}$ value and average value of the voltage.

• A. $0.63$
• B. $1.63$
• C. $1$
• D. $0$

Answer 1

The correct option is B $1.63$

By looking the given waveform, For a time period of $T=4\text{sec}$.

$$V=\{\begin{array}{cc}1.5t& \text{for}0\le t\le 2\\ 0& \text{for}2<t\le 4\end{array}$$

$V_{av}=\frac{1}{T}{\int }_0^{T}Vdt=\frac{1}{4}{\int }_0^{2}1.5tdt=\frac{1}{4}\times [\frac{1.5t^2}{2}{]}_0^2=0.75\text{volts}$

$V_{rms}=[\frac{1}{T}{\int }_0^T{V}^{2}dt{]}^{\frac{1}{2}}=[\frac{1}{4}{\int }_0^2(1.5t{)}^{2}dt{]}^{\frac{1}{2}}=1.22\text{volts}$

$\therefore \frac{V_{rms}}{V_{av}}=\frac{1.22}{0.75}=1.63$