Question

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 $220V$ supply line one by one , what will be the ratio of electric power consumed by them ?

Answer 1

Let resistance of each lamp = R ohms.
Case 1 : Parallel connection
Resultant resistance = $\frac{1}{1/R+1/R}=\frac{R}{2}$
Electric power consumed $P_1=\frac{V^2}{R}=\frac{{220}^2}{R/2}=\frac{96800}{R}$
Case 2 : Series connection
Resultant resistance = $R+R=2R$
Electric power consumed $P_2=\frac{V^2}{2R}=\frac{24200}{R}$
$\therefore \frac{P_1}{P_2}=\frac{96800}{R}/\frac{24200}{R}=\frac{4}{1}$