A current is made of two components a dc component i1 = 3 A and an ac component i2 = 4√2 sin ωt. Find the reading of hot wire ammeter?

Q: A current is made of two components a dc component i1 = 3 A and an ac component i2 = 4√2 sin ωt. Find the reading of hot wire ammeter ?

Sol: $\large i = i_1 + i_2 $

$\large i = 3 + 4 \sqrt{2} sin\omega t $

$\Large i_{rms}^2 = \frac{\int_{0}^{T} i^2 dt}{\int_{0}^{T} dt} $

$\Large i_{rms}^2 = \frac{\int_{0}^{T} (3 + 4 \sqrt{2} sin\omega t)^2 dt}{T} $

$\Large i_{rms}^2 = \int_{0}^{T} (9 + 24 \sqrt{2} sin\omega t + 32 sin^2 \omega t) dt $

irms = 5 A