An AC current is given by I = I₁ sinωt + I₂ cosωt. A hot wire ammeter will give a reading :

Solution

Physics sir · 3 steps

A hot wire ammeter reads the rms value, so square the current, average it over a cycle, then take the root.

1. What it measures. A hot wire ammeter works by heating, and heat depends on I². So it shows the rms current, Iᵣₘₛ = √(⟨ I² ⟩).

   I² = I₁²sin² ω t + I₂²cos² ω t + 2I₁I₂sin ω t cos ω t

2. Average each term. Over one full cycle, ⟨ sin² ω t ⟩ = ⟨ cos² ω t ⟩ = 1/2. The cross term is I₁I₂sin 2ω t, which averages to zero. So ⟨ I² ⟩ = (I₁² + I₂²)/2.
3. So. Iᵣₘₛ = √((I₁² + I₂²)/2), which is option (c).

The idea to keep. Sine and cosine of the same ω are 90° apart, so they combine like perpendicular vectors: the peak is √(I₁² + I₂²), and rms is that peak divided by √2.

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