An ac current is represented as $i=5\sqrt{2}+10 \cos \left(650 \pi t+\frac{\pi}{6}\right)$ Amp The r.m.s value of the current is

JEE Main · 2025 · 07 Apr 2025 · Shift 1 · Alternating Current

An ac current is represented as

i = 52 + 10 cos (650 π t + \frac{π}{6})

Amp

The r.m.s value of the current is

(A)50 Amp
(B)100 Amp
(C)10 Amp✓ Correct
(D) $52$ Amp

Answer: (C)

Solution

The current is a steady part

52

A plus a sinusoid of amplitude

10

A. The mean square of a constant is its square, the mean square of a sinusoid is half its squared amplitude, and the average of the cross term vanishes:

⟨ i^{2} ⟩ = (52)^{2} + \frac{1 0 ^{2}}{2} = 50 + 50 = 100 A^{2} .

The r.m.s. value is the square root of this mean square:

i_{r m s} = 100 = 10 A .

The r.m.s. value of the current is

10

JEE Main · 2025 · 07 Apr 2025 · Shift 1 · Single correct option

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