Question

A choke coil is needed to operate an arc lamp at $160\text{V}$ $\left(rms\right)$ and $50\text{Hz}$. The lamp has an effective resistance of $5\Omega$ when running at $10\text{A}$ $\left(rms\right)$. If the inductance of the chock coil is $\frac{76k}{1000\pi }\text{H}$, the value of $k$ is

(integer only)

Answer 1

For lamp,

$(V_{rms}{)}_R=i_{rms}\cdot R=10\times 5=50\text{V}$


In series,

$(V_{rms}{)}^2=(V_{rms}{)}_R^2+(V_{rms}{)}_L^2$

$\therefore (V_{rms}{)}_L=\sqrt{(V_{rms}{)}^2-(V_{rms}{)}_R^2}=\sqrt{(160{)}^2-(50{)}^2}$

$\Rightarrow (V_{rms}{)}_L=152\text{V}$

As, $(V_{rms}{)}_L=(i_{rms})\cdot X_L=(i_{rms})\cdot (2\pi fL)$

$\therefore L=\frac{(V_{rms}{)}_L}{\left(2\pi f\right)\cdot \left(i_{rms}\right)}$

Substituting the values, we get

$L=\frac{152}{\left(2\pi \right)\left(50\right)\left(10\right)}=\frac{152}{1000\pi }\text{H}$

Given, $L=\frac{76k}{1000\pi }\text{H}$

$\Rightarrow 76k=152$

$\therefore k=2$