Question

Two exactly similar electric lamps are arranged first in parallel, and then in series. If the parallel and series combinations of lamps were connected to $220\text{V}$ supply, what will be the ratio of electric power consumed in parallel and series combinations?

• A. $1:3$
• B. $4:1$
• C. $1:2$
• D. $5:1$

Answer 1

The correct option is B $4:1$

Let the resistance of each lamp is $R$.

For parallel combination :

$R_{\text{eq}}=\frac{R\times R}{R+R}=\frac{R}{2}$

Electric power consumed,

$P_1=\frac{V^2}{R_{\text{eq}}}=\frac{{220}^2\times 2}{R}$

For series combination :

$R_{\text{eq}}^{\prime }=R+R=2R$

Electric power consumed,

$P_2=\frac{V^2}{R_{\text{eq}}^{\prime }}=\frac{{220}^2}{2R}$

Now,

$\frac{P_1}{P_2}=\frac{\frac{{220}^2\times 2}{R}}{\frac{{220}^2}{2R}}=\frac{4}{1}=4:1$

​​​​​​​Hence, option $\left(B\right)$ is the correct answer.