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` ?

Explanation

First we will calculate the resistance (R) of one bulb by using the given power (P) and voltage (V) values.
Now, Power, `P = (V^(2))/(R)`
So, `10 = ((220)^(2))/(R)`
And, `R = (220 xx 220)/(10)`
Resistance of 1 bulb, `R = 4840 Omega`
We will now calculated the total resistance of the circuit by using the given V (voltage) and I (current) values.
Now, `(V)/(I)= R`
So, `(220)/(5) = R`
Total resistance, `R = 44 Omega`
Thus, the total resistance of the circuit is 44 ohms. Now, all that we have to do is to find out how many `4840 Omega` bulbs should be connected in parallel to obtain a total resistance of `44 Omega`. Suppose the number of `4840 Omega` bulbs required is x. Then:
`(1)/(44) = (1)/(4840) xx x` (Resistance in parallel)
`x = (4840)/(44)`
`x = 110`
Thus, 110 bulbs can be connected in parallel in this circuit.