Two lamps, one is rated $100\, W$ at $220\, V$, and the other $60 \,W$ at $220\, V ,$ are connected in parallel to a $220\, V$ supply. Find the current drawn from the supply line.

Resistance of first lamp $= R _{1}$

Resistance of second lamp $= R _{2}$

We know that

$R=\frac{V^{2}}{P}$

$R_{1}=\frac{220 \times 220}{100}=484 \Omega$

$R_{2}=\frac{220 \times 220}{60}=\frac{2420}{3} \Omega$

When $R _{1}$ and $R _{2}$ are connected in parallel

$\frac{1}{R}=\frac{1}{R_{1}}+\frac{1}{R_{2}}$

$(R$ is the equivalent resitance)

$\Rightarrow \quad R=\frac{R_{1} R_{2}}{R_{1}+R_{2}}=\frac{484 \times \frac{2420}{3}}{484+\frac{2420}{3}}$

$=\frac{484 \times \frac{2420}{3}}{484\left(1+\frac{5}{3}\right)}=\frac{2420 \times 3}{8 \times 3}=\frac{605}{2} \Omega$

$I =\frac{ V }{ R }=\frac{220}{\frac{605}{2}}=\frac{220 \times 2}{605}$

$I =\frac{8}{11} A =0.727 A$