Question

Two resistances $R_{1}$ and $R_{2}$ when connected in series and parallel with 120 V line, power consumed will be 25 W and 100 W respectively. Then the ratio of power consumed by $R_{1}$ to that consumed by $R_{2}$ will be

• A. 1 : 1
• B. 1 : 2
• C. 2 : 1
• D. 1 : 4

Answer 1

Answer: (A)

1 : 1

Answer 2

$P = \frac{V^{2}}{R}$⇒ $\frac{P_{P}}{P_{S}} = \frac{R_{S}}{R_{P}} = \frac{(R_{1} + R_{2})}{R_{1}R_{2}/(R_{1} + R_{2})} = \frac{(R_{1} + R_{2})^{2}}{R_{1}R_{2}}$

⇒ $\frac{100}{25} = \frac{(R_{1} + R_{2})^{2}}{R_{1}R_{2}}$ ⇒ $\frac{R_{1}}{R_{2}} = \frac{1}{1}$