Question

An electric bulb is designed to consume $55W$ when operated at $110volts$. If is connected to a $220V,50Hz$ line through a choke coil in series. What should be the inductance of the coil for which the bulb gets correct voltage?

Answer 1

We know that,

$I=\frac{p}{v}=\frac{55}{110}=\frac{1}{2}A$

So, $p=\frac{v^2}{R}\Rightarrow R=\frac{V^2}{p}=\frac{{110}^2}{55}=220\Omega$

A/C $220v,t=50Hz$

Therefore,

$I=\frac{v}{z}=\frac{v}{\sqrt{R^2+x_l^2}}=\frac{v}{\sqrt{R^2+({\omega }_l{)}^2}}\Rightarrow \frac{1}{4}$

$=\frac{{220}^2}{({220}^2+2\times \pi \times 50\times l{)}^2}\Rightarrow {220}^2+4\times 10\times 2500l^2=4\times {220}^2$

$\Rightarrow {10}^5{l}^2={220}^2\times 3=\Rightarrow l^2=\frac{48400\times 3}{{10}^5}\Rightarrow l=1.2H$