Question 342: AC fundamentals

Question

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 $\pi=\frac{22}{7}$ ]

Accepted Answer

To find the r.m.s. value of the current in the circuit, first calculate the inductive reactance ($X_L$) using the formula:
$$ X_L = 2 \pi f L $$
where:
$ f = 50 \, 	ext{Hz} $ is the frequency,
$ L = 42 \, 	ext{mH} = 42 	imes 10^{-3} \, 	ext{H} $ is the inductance,
$ \pi = \frac{22}{7} $.
Substitute the given values:
$$ X_L = 2 	imes \frac{22}{7} 	imes 50 	imes 42 	imes 10^{-3} $$
$$ X_L = \frac{44}{7} 	imes 50 	imes 42 	imes 10^{-3} $$
Calculate $ X_L $:
$$ X_L = \frac{44 	imes 50 	imes 42}{7 	imes 1000} $$
$$ X_L = \frac{92400}{7000}  $$
$$ X_L \approx 13.2 \, \Omega $$
The r.m.s. current $ I $ can be calculated using Ohm's Law for AC circuits:
$$ I = \frac{V}{X_L} $$
where $ V = 200 \, 	ext{V} $.
Substitute the values:
$$ I = \frac{200}{13.2} $$
Calculate $ I $:
$$ I \approx 15.15 \, 	ext{A} $$
Thus, the r.m.s. value of the current in the circuit is approximately $ 15.15 \, \mathrm{A} $.
The correct option is:
Option A: $ 15.15 \, \mathrm{A} $

Answer

$15.15 \mathrm{~A}$

Answer

$9.15$ A

Answer

$8.15$ A

Answer

$6 . 15 \mathrm{~A}$

AC fundamentals

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} ]

Choose the correct answer: