Question

Several electric bulbs designed to be used on a $220V$ electric supply line, are rated 10 W. How many lamps can be connected in parallel with each other across the two wires of $220V$ line if the maximum allowable current is $5A$?

• A. $22$
• B. $5$
• C. $48$
• D. $110$

Answer 1

The correct option is D $110$

Given : $P=10$ W $V=220$ volts $I=5$ A

Total resistance of the circuit $R_{eq}=\frac{V}{I}=\frac{220}{5}=44\Omega$

Resistance of each bulb $R=\frac{V^2}{P}=\frac{(220{)}^2}{10}=4840\Omega$

Let $n$ bulbs each of resistance $R$ is connected in parallel which gives $R_{eq}$ as the total resistance of the circuit.

$\therefore$ $R_{eq}=\frac{R}{n}$

$⟹$ Number of bulbs $n=\frac{R}{R_{eq}}=\frac{4840}{44}=110$