Question

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

The resistance of bulb can be calculated by the formula-

$P=\frac{V²}{R}$

So,

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

$=220\ast 220/10$

$=4840\Omega$

Now coming on to the circuit,

$V=220V$

$I=5A$

So by Ohm's law, we get-

$R=V/I=220/5=44\Omega$

Let there be n resistances of $4840\Omega$ in parallel and net resistance $=44\Omega$

So,

$1/44=1/4840+1/\mathrm{4840...}n$ times

This implies that,

$R=4840/n$

$4840/n=44$

Therefore $n=110.$

This tells us that $110$ bulbs can be connected in parallel.