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

(C) $100 \mathrm{~A}, 50 \mathrm{~Hz}$

(A) $100 \sqrt{2} \mathrm{~A}, 100 \mathrm{~Hz}$

(B) $\frac{100}{\sqrt{2}} \mathrm{~A}, 100 \mathrm{~Hz}$

(D) $50 \sqrt{2} \mathrm{~A}, 50 \mathrm{~Hz}$

JEE Main · 2025 · 04 Apr 2025 · Shift 1 · Alternating Current

An alternating current is represented by the equation,

i = 1002 sin (100 π t)

ampere. The RMS value of current and the frequency of the given alternating current are

Answer: (C)

For a sinusoidal current

i = i_{0} sin (ω t)

, the root-mean-square value is

i_{r m s} = i_{0} / 2

. With peak value

i_{0} = 1002

i_{r m s} = \frac{100 2}{2} = 100 A .

The angular frequency read from the argument is

ω = 100 π

rad/s, so

f = \frac{ω}{2 π} = \frac{100 π}{2 π} = 50 Hz .

The current has an rms value of

100

A and a frequency of

50

Hz.

JEE Main · 2025 · 04 Apr 2025 · Shift 1 · Single correct option