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An a.c. current is I=I₁ sin ω t+I₂ cos ω t. A hot-wire ammeter reads

Asked in JEE Main 17th March 1st Shift 2021 · Measuring AC quantities

(1) (I₁+I₂)/(2√2)
(2) √(I₁²+I₂²)/2
(3) √(I₁²-I₂²)/2
(4) (I₁+I₂)/(√2)

Answer: (2) √(I₁²+I₂²)/2

Step-by-step solution

I₁ sin ω t+I₂ cos ω t has resultant amplitude I₀=√I₁²+I₂².

A hot-wire ammeter reads r.m.s.: Iᵣₘₛ=(I₀)/(√2)=√(I₁²+I₂²)/2.

Why the other options are wrong

(1) Averages the amplitudes instead of combining their squares.
(3) Subtracts the squares instead of adding them.
(4) Adds the amplitudes rather than the resultant of a sine and cosine.

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