Question

Two lamps , one rated $100W$ at $220V$, and the other $60W$ at $220V$, are connected in parallel to electric mains supply. What current is drawn from the line if the supply voltage is $220V$?

Answer 1

We know that, $P=\frac{V^2}{R}$

From the figure,

$R_1=\frac{V_1^2}{P_1}=\frac{220\times 220}{100}$

$R_1=484\Omega$

$R_2=\frac{V_1^2}{P_2}=\frac{220\times 220}{60}$

$R_2=806.7\Omega$

The equivalent resistance in parallel combination,

$\frac{1}{R_{eq}}=\frac{1}{R_1}+\frac{1}{R_2}$

$\frac{1}{R_{eq}}=\frac{1}{484}+\frac{1}{806.7}$

$R_{eq}=302.5\Omega$

The current flowing in the circuit,

$I=\frac{V}{R_{eq}}=\frac{220}{302.5}$

$I=0.7272A$