Question

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

Answer 1

Answer:  0.7273 A

Explanation:

From Joule's Law of heating,  power    $P = \frac{V^2}{R}$

Where V is the voltage and R is the resistance.

For first lamp, the resistance is obtained as:

$R_1 = \frac{(220)^2}{100}$

For second lamp, the resistance is obtained as:

$R_2 = \frac{(220)^2}{60}$

When they are connected in parallel, the equivalent resistance $R_{eq}$ is

$1/R_{eq} = 1/R_1 +1/ R_2\\ \\or, 1/ R_{eq} = 1/ \frac{(220)^2}{100} + 1/ \frac{(220)^2}{60}\\\\or, R_{eq} = \frac{(220)^2}{160}$

Let, the current is drawn from the line is I. So, from Ohm's Law,

$V = I ~ R_{eq}$

So the current is given by,

​$I = \frac{V}{R_{eq}} = 220 \times \frac{160}{(220)^2} \\\\= 0.7273 ~A$