The alternating current is given by i = { √42 sin ( 2π/Tt ) + 10 }A
The r.m.s. value of of this current is ................. A.

Solution

Physics sir · 3 steps

RMS means mean of the square, so square the whole current and average it over one full period.

1. Square the current. i² = 42 sin²((2π t)/T) + 20√42 sin((2π t)/T) + 100. The rms value is the square root of the average of this over one period.
2. Average each term. Over a full period the average of sin² is 1/2 and the average of sin is 0. So the cross term drops out, and the steady 10 A part keeps its full 100.

   iᵣₘₛ² = 42 × 1/2 + 0 + 100 = 121

3. So. iᵣₘₛ = √121 = 11 A.

The common slip: 12. Forgetting that sin² averages to 1/2 gives √(42 + 100) = √142 ≈ 11.9, which rounds to 12 instead of 11.

The idea to keep. For a DC part plus a sine part, iᵣₘₛ = √(I_(dc)² + I₀²/2). Add the squares, never the two rms values directly.

Answer from the NTA final answer key. Solution by PrepWiser.