Question

A 200 V, 100 Watt bulb is to be used across an A.C source of peak voltage 400 V and an angular frequency of ${10}^3$ rad/s. The inductance of a choke coil to be used in series with the bulb so that the bulb won't blow off is

Answer 1

By $p=vi\Rightarrow i=\frac{100}{200}=\frac{1}{2}=i_{rms}$ for an AC source.
$p=\frac{v^2}{R}\Rightarrow R=400\Omega$ i.e., resistance of bulb.
$i_{rms}=\frac{i_0}{\sqrt{2}}=\frac{{\epsilon }_0}{\sqrt{2}z}=\frac{{\epsilon }_0}{\sqrt{2}\sqrt{(\omega L{)}^2+R^2}}$
$\frac{1}{2}=\frac{400}{\sqrt{2}\sqrt{(\omega L{)}^2+{400}^2}}\Rightarrow \omega L=400\Rightarrow L=0.4H$