An alternating current is given by $\mathrm{i}=(3 \sin \omega t+4 \cos \omega t)$ A. The $r m s$ current…

An alternating current is given by $\mathrm{i}=(3 \sin \omega t+4 \cos \omega t)$ A. The $r m s$ current will be
  1. $\frac{7}{\sqrt{2}} A$
  2. $\frac{1}{\sqrt{2}} A$
  3. $\frac{5}{\sqrt{2}} A$
  4. $\frac{3}{\sqrt{2}} A$

Solution

$i=(3 \sin w t+4 \cos w k) A$ $\therefore$ Peak current, $\mathrm{I}_0=\sqrt{3^2+4^2}=5 \mathrm{~A}$ $\therefore \quad$ RMS current, $\mathrm{I}_{\mathrm{rms}}=\frac{\mathrm{I}_{\mathrm{o}}}{\sqrt{2}}=\frac{5}{\sqrt{2}} \mathrm{~A}$

Asked in: AP EAMCET 2024 (23 May Shift 1)

Practice more Alternating Current questions on Aicharya