A 42 mH inductor is connected to $200 \mathrm{~V}, 50 \mathrm{~Hz}$ a.c. supply. The r.m.s. value of current…

A 42 mH inductor is connected to $200 \mathrm{~V}, 50 \mathrm{~Hz}$ a.c. supply. The r.m.s. value of current in the circuit will be nearly [ Take $\pi=\frac{22}{7}$ ]
  1. $15.15 \mathrm{~A}$
  2. $9.15 \mathrm{~A}$
  3. 8.15 A
  4. 6.15 A

Solution

$\begin{aligned} \mathrm{X}_{\mathrm{L}} & =\omega \mathrm{L} \\ & =2 \pi \mathrm{~F} . \mathrm{L} \\ & =2 \times \pi \times 50 \times 42 \times 10^{-3} \\ & =13.194 \Omega \\ \mathrm{I}_{\mathrm{RMS}} & =\frac{\mathrm{V}}{\mathrm{X}_{\mathrm{L}}}=\frac{200}{13.194}=15.15 \mathrm{~A}\end{aligned}$

Asked in: MHT CET 2024 (03 May Shift 2)

Practice more Alternating Current questions on Aicharya