Q137 / 180 · COMEDK 2015 · Physics

If instantaneous current is given by $i=4 \cos (\omega t+\phi)$, then the rms value of current is

  • Correct answer
    A
    $2 \sqrt{2} \mathrm{~A}$
  • B
    $4 \mathrm{~A}$
  • C
    $4 \sqrt{2} \mathrm{~A}$
  • D
    zero

Solution

Instantaneous current, $$ i=4 \cos (\omega t+\phi) $$ Comparing with standard equation, $i=i_{0} \cos (\omega t+\phi)$, we get $\therefore$ Peak current, $i_{0}=4 \mathrm{~A}$ $$ \text { Hence, } \begin{aligned} i_{\mathrm{rms}} &=\frac{i_{0}}{\sqrt{2}} \\ &=\frac{4}{\sqrt{2}}=2 \sqrt{2} \mathrm{~A} \end{aligned} $$

Hence, the correct answer is option: 'A'.

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