Question

When two resistances $R_1$ and $R_2$ are connected in series, they consume 12W power. When they are connected in parallel, they consume 50W power. What is the ratio of the powers of $R_1$ and $R_2$

• A. $1/4$
• B. $4$
• C. $3/2$
• D. $3$

Answer 1

The correct option is C $3/2$

Let the powers of the resistances be $P_1$ and $P_2$.

Parallel connection : $P_{eq}=P_1+P_2$

$\therefore$ $50=P_1+P_2$ $⟹P_2=50-P_1$

Series connection : $P_{eq}=\frac{P_1{P}_2}{P_1+P_2}$

$\therefore$ $12=\frac{P_1(50-P_1)}{50}$

OR $P_1^2-50P_1+600=0$ $⟹$ $P_1=30$ W

$⟹$ $P_2=50-30=20$ W

Thus ratio of powers $\frac{P_1}{P_2}=\frac{3}{2}$