Question

For the waveform given below


The $\text{rms}$ value of the wave form is given by

• A. $10\sqrt{7}$
• B. $\frac{10}{\sqrt{3}}$
• C. $10\sqrt{\frac{7}{3}}$
• D. $10\sqrt{3}$

Answer 1

The correct option is C $10\sqrt{\frac{7}{3}}$


From above graph, the variation of Voltage $V$ with time $t$ is

$V=10+\left(\frac{10}{T}\right)t$

Now, the $\text{rms}$ value of voltage is

$V_{\text{rms}}^2=\frac{1}{T}{\int }_0^T{V}^{2}dt$

$\Rightarrow V_{\text{rms}}^2={\int }_0^T{(10+\frac{10t}{T})}^{2}dt$

$\Rightarrow V_{\text{rms}}^2=\frac{1}{T}{\int }_0^T(100+\frac{100t^2}{T^2}+\frac{200t}{T})dt$

$\Rightarrow V_{\text{rms}}^2=\frac{700}{3}$

$\Rightarrow V_{\text{rms}}=10\sqrt{\frac{7}{3}}$

Hence, option $\left(\text{C}\right)$ is correct.