An ac current is represented as i = 5√(2) + 10 cos (650π t + π/6) Amp The r.m.s value of the current is (a) 10 Amp (b) 5√(2) Amp (c) 100 Amp (d) 50 Amp

Answer: (a). For i = Idc + I₀cos (ω t + φ): Irms² = Idc² + (I₀²)/(2) (cross term averages to zero). Irms² = (5√(2))² + 10²/2 = 50 + 50 = 100 Irms = 10 A So the answer is (a) 10 Amp.

An ac current is represented as i = 5√(2) + 10 cos (650π t + π/6) Amp… | JEE Main 2025 (7 Apr, Shift 1)

Q10JEE Main 2025 · 7 APR · SHIFT 1Easy

AC Basics: Peak, RMS & Average Values

An ac current is represented as

$i = 5\sqrt{2} + 10 \cos\left(650\pi t + \frac{\pi}{6}\right)\text{ Amp}$

The r.m.s value of the current is

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Answer: (a)

For $i = I_{dc} + I_0\cos(\omega t + \phi)$ : $I_{rms}^2 = I_{dc}^2 + \frac{I_0^2}{2}$ (cross term averages to zero).
$I_{rms}^2 = (5\sqrt{2})^2 + \frac{10^2}{2} = 50 + 50 = 100$
$I_{rms} = 10$ A
So the answer is (a) 10 Amp.

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