Question

The rms and the average value of the voltage wave shown in the figure are

• A. $\sqrt{\frac{32}{3}}V;1V$
• B. $\sqrt{\frac{11}{3}}V;1V$
• C. $\sqrt{\frac{11}{3}}V;3V$
• D. $\sqrt{\frac{32}{3}}V;3V$

Answer 1

The correct option is D $\sqrt{\frac{32}{3}}V;3V$

RMS voltage

$\begin{array}{cc}\Rightarrow Vrms=\sqrt{\frac{{\left(sumofmidordinate\right)}^2}{numberofordinate}}& \\ \Rightarrow Vrms=\sqrt{\frac{4^2+4^2}{3}}& =\sqrt{\frac{32}{3}}\end{array}$

As we know that

$\begin{array}{c}\Rightarrow Vrms=\frac{\pi }{2\sqrt{2}}Vavg=1.11Vavg\\ \Rightarrow \sqrt{\frac{32}{3}}V=0.11Vavg\\ \Rightarrow Vavg=\frac{\sqrt{32/3}}{1.11}=2.97\simeq 3V\end{array}$