Question

A choke coil is needed to operate an arc lamp at $250\text{V}$(rms) and $50\text{H}z$. The lamp has an effective resistance of $15\Omega$ when running at $10\text{A}$ (rms). The inductance of the choke coil is $\frac{N}{125\pi }\text{H}$. Find the value of $N$.

• A. 25.0
• B. 25
• C. 25.00

Answer 1

Answer: (A), (B), (C)

We have, voltage across resistance
${\left(V_{rms}\right)}_R=i_{rms}R=150\text{V}$
We know that
$V_{rms}^2=(V_{rms}{)}_L^2+(V_{rms}{)}_R^2$

$\therefore$${\left(V_{rms}\right)}_L=\sqrt{V_{rms}^2-(V_{rms}{)}_R^2}=\sqrt{{250}^2-{150}^2}=200\text{V}$
${\left(V_{rms}\right)}_L=i_{rms}{X}_L=i_{rms}2\pi fL$
$\Rightarrow L=\frac{200}{10\times 2\pi \times 50}=\frac{1}{5\pi }\text{H}=\frac{25}{125\pi }\text{H}$
$\therefore$ value of $N=25$