Chapter 3: Electricity

Q&A -Ask Doubts and Get Answers



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?


The resistance of each bulb R can be calculated using the relation,

P = frac{V^2}{R}

R = frac{V^2}{P}

It is given,

P = 10 W

V = 220 V

R = frac{(220)^2}{10}

R = frac{220 	imes 220}{10}

R = 4840 Omega

So, the resistance of each bulb is 4840 Omega.

Let the number of lamps be x.

When lamps are connected in parallel, the equivalent resistance R_{eq} will be,

frac{1}{R_{eq}} = frac{1}{4840} + frac{1}{4840} + frac{1}{4840} -----x times

frac{1}{R_{eq}} = frac{1 + 1 + 1 + ----x times}{4840}

frac{1}{R_{eq}} = frac{x}{4840}

R_{eq} = frac{4840}{x}-------(1)

V = 220 V {Given}

I = 5 A {Given}

Using ohms law,

V = IR_{eq}

R_{eq} = frac{V}{I}

R_{eq} = frac{220}{5}

R_{eq} = 44 Omega

Putting the value of R_{eq} in equation (1), we get

44 = frac{4840}{x}

x = frac{4840}{44}

x = 110

Therefore, 110 electric bulbs are connected in parallel.

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