Question

Question 12
Several electric bulbs designed to be used on a 220 V electric supply line, are rated 10 W. How many lamps can be connected in parallel with each other across the two wires of 220 V line if the maximum allowable current is 5 A?

Answer 1

Resistance $R_1$ of the bulb is given by the expression,
Supply voltage, V = 220 V
Maximum allowable current, I = 5 A
Rating of an electric bulb, P = 10 Watts
Because $R=\frac{V^2}{P}$
$R_1=\frac{(220{)}^2}{10}=4840\Omega$
According to Ohm's law, V = IR
Let R is the total resistance of the circuit for X number of electric bulbs.
R = $\frac{V}{I}$ $=\frac{220}{5}=44\Omega$
Resistance of each electric bulb, $R_1=4840\Omega$
$\frac{1}{R}=\frac{1}{R_1}+\frac{1}{R_2}+....uptoXtimes$.
$\frac{1}{R}=\frac{1}{R_1}\times X$
$X=\frac{R_1}{R}=\frac{4840}{44}=110$
$\therefore$ Number of electric bulbs connected in parallel are 110.