Answer in Brief

Sum

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?

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#### Solution

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=10watts

Because R=V^{2}/P

`R_1=(220)^2/10=4840`

According to Ohm's law

V=IR

Let R is the total resistance of the circuit for x number of electric bulbs

`R=V/I`

`=220/5=44Omega`

Resistance of each electric bulb, R_{1}=4840Ω

`1/R=1/R_1+1/R_2+`.......Upto x times

`1/R=1/Rxx x`

`x=R_1/R=4840/44=110`

∴ Number of electric bulbs connected in parallel are 110.

Concept: System of Resistors - Resistances in Parallel

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