Question

If instantaneous current in a circuit is given by $I=(2+3\sin \omega t)A$, then the effective value of resulting current in the circuit is?

• A. $\sqrt{\frac{17}{2}}$A
• B. $\sqrt{\frac{2}{17}}$A
• C. $\sqrt{\frac{3}{\sqrt{2}}}$A
• D. $3\sqrt{2}$A

Answer 1

The correct option is A $\sqrt{\frac{17}{2}}$A

Given,

Instantaneous current, $i=2+3\sin \omega t$

$i_{rms}=\sqrt{\frac{1}{T}{\int }_0^T{(2+3\sin \omega t)}^{2}dt}$

$i_{rms}=\sqrt{\frac{1}{T}{\int }_0^T(2^2+3^2{\sin }^2\omega t+12\sin \omega t)dt}$

$i_{rms}=\sqrt{\frac{1}{T}\left[{\int }_0^T{2}^{2}dt+{\int }_0^T{3}^2(\frac{1}{2}-\frac{\cos 2\omega t}{2})dt+{\int }_0^T\left(12\sin \omega t\right)dt\right]}$

$i_{rms}=\sqrt{4+\frac{9}{2}+0}=\sqrt{\frac{17}{2}}A$

Hence, resulting current is $\sqrt{\frac{17}{2}}A$