An alternating current is represented by the equation, $i=100 \sqrt{2} \sin (100 \pi t)$ ampere. The RMS…

An alternating current is represented by the equation, $i=100 \sqrt{2} \sin (100 \pi t)$ ampere. The RMS value of current and the frequency of the given alternating current are
  1. $100 \sqrt{2} \mathrm{~A}, 100 \mathrm{~Hz}$
  2. $\frac{100}{\sqrt{2}} \mathrm{~A}, 100 \mathrm{~Hz}$
  3. $100 \mathrm{~A}, 50 \mathrm{~Hz}$
  4. $50 \sqrt{2} \mathrm{~A}, 50 \mathrm{~Hz}$

Solution

$\begin{aligned} & \mathrm{i}_{\mathrm{r}}=\frac{\mathrm{i}_0}{\sqrt{2}}=100 \mathrm{~A} \\ & \mathrm{f}=\frac{\mathrm{w}}{2 \pi}=\frac{100 \pi}{2 \pi}=50 \mathrm{~Hz}\end{aligned}$

Asked in: JEE Main 2025 (04 Apr Shift 1)

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