First slide

Electrical power

Question

Two resistances R₁ and R₂ 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 R₁ to that consumed by R₂ will be

Easy

A

1 : 1
B

1 : 2
C

2 : 1
D

1 : 4

Solution

$\begin{array}{l} P = \frac{V^{2}}{R} \Rightarrow \frac{P_{P}}{P_{S}} = \frac{R_{S}}{R_{P}} = \frac{(R_{1} + R_{2})}{R_{1} R_{2} / (R_{1} + R_{2})} = \frac{{(R_{1} + R_{2})}^{2}}{R_{1} R_{2}} \\ \Rightarrow \frac{100}{25} = \frac{{(R_{1} + R_{2})}^{2}}{R_{1} R_{2}} \Rightarrow \frac{R_{2}}{R_{1}} = \frac{1}{1} \end{array}$

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