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Question

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


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Solution

Step 1: Given

Voltage V=220V and power P=10W.

Current I=5A

Step 2: Calculate resistance for each lamp

We know the relation,

P=V2R'

Where R' is the resistance.

R'=V2P

Upon substituting the values we get,

R'=220210

=4840010

=4840Ω

Step 3: Calculate equivalent resistance

According to Ohm's law,

V=IR

R=VI

Upon substituting the values we get,

R=2205

=44Ω

Step 4: Calculate total number of lamps

The resistance of each electric bulb, R'=4840Ω

We know that resistances in parallel connection are given as,

1R=1R1+1R2+.....x times

144=1R'×x

x=484044

=110

Hence, 110 lamps can be connected in parallel.


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