Two exactly similar electric lamps are arranged (i) in parallel, and (ii) in series. If the parallel and series combination of lamps are connected to 220 V supply line one by one, what will be the ratio of electric power consumed by them?

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Solution

Let R be the resistance of the lamp and V be the potential difference applied.

In a series connection:
Net resistance of the circuit, R₁ = R + R = 2R
Power drawn, P₁ = V²/R₁ = V²/2R
In a parallel connection:
Net resistance of the circuit, R₂ will be:
$\frac{1}{R_{2}} = \frac{1}{R} + \frac{1}{R} = \frac{2}{R}$
or R₂ = $\frac{R}{2}$
Power drawn, P₂ = V²/R₂ = 2V²/R
Therefore, P₂:P₁ = 4:1

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