Question

The electric current in A.C. circuit is given by the relation $i=3\sin \omega t+4\cos \omega t$. The rms value of the current in the circuit in amperes is:

• A. $\frac{5}{\sqrt{2}}$
• B. $5\sqrt{2}$
• C. $\frac{2}{\sqrt{5}}$
• D. $\frac{1}{\sqrt{2}}$

Answer 1

The correct option is A $\frac{5}{\sqrt{2}}$

AC current is expressed here as $i=3sin\omega t+4cos\omega t$

$=5(\frac{3}{5}sin\omega t+\frac{4}{5}cos\omega t)$

$=5sin(\omega t+\varphi )$

where $\varphi =ta{n}^{-1}\frac{4}{3}$

Hence amplitude of AC current is $5A$.
$I_{rms}=\frac{I_0}{\sqrt{2}}$

Thus, rms value of AC current is $\frac{5}{\sqrt{2}}A$