Question

A $20$ volt $5$ watt lamp is used on a.c mains of $200$ volts $50$ c.p.s. Calculate the value of
(a) capacitance (b) inductance to be put in series to run the lamp
(c) how much pure resistance should be included in place of the above device so that lamp can run on its voltage?

Answer 1

For lamp $I=\frac{5}{20}0.25A;R=\frac{20}{0.25}=80\Omega$
Current through the lamp should be $0.25A$
(a) when condenser $C$ is placed in series
$i=\frac{200}{\sqrt{R^2+{\left(\frac{1}{\omega C}\right)}^2}}=0.25$
putting the value of $\omega =2\pi \times 50$
$\therefore C=4.0\mu F$
(b) when inductor is used
$I=\frac{200}{\sqrt{R^2+{\left(\omega L\right)}^2}}=0.25\Rightarrow L=2.53H$
(c) when resistance is used
$I=\frac{200}{R+r}=0.25\Rightarrow r=720\Omega$