Question

In a circuit, an alternating current and direct current are supplied together. The expression of the instantaneous current is given as $i=3+6\sin \omega t.$ Then, the rms value of the current is:

• A. $3A$
• B. $6A$
• C. $3\sqrt{2}A$
• D. $3\sqrt{3}A$

Answer 1

The correct option is D $3\sqrt{3}A$

Given,

Instantaneous current, $i=3+6\sin \omega t$

$i_{rms}=\sqrt{\frac{1}{T}{\int }_0^T{(3+6\sin \omega t)}^{2}dt}$

$i_{rms}=\sqrt{\frac{1}{T}{\int }_0^T(3^2+6^2{\sin }^2\omega t+36\sin \omega t)dt}$

$i_{rms}=\sqrt{\frac{1}{T}\left[{\int }_0^T{3}^{2}dt+{\int }_0^T{6}^2(\frac{1}{2}-\frac{\cos 2\omega t}{2})dt+{\int }_0^T\left(36\sin \omega t\right)dt\right]}$

$i_{rms}=\sqrt{9+\frac{36}{2}+0}=3\sqrt{3}A$

Hence, RMS value of current is $3\sqrt{3}A$