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Heating Effect of Electric Current

A simple circ...

Question

A simple circuit consisting of three resistors is shown above. $R_{1}$ has the same resistance of $R_{2}$ and $R_{2}$ has twice the resistance of $R_{3}$ . If the switch remains closed, determine the ratio of heat dissipated of $R_{1}$ to $R_{2}$ .

1:9

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1:3

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1:1

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3:1

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9:1

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Solution

The correct option is E 9:1
$R_{1} = R_{2} = 2 R_{3} = 2 R (l e t)$
Let the current in $R_{1}$ be $i$ .
Then current in $R_{2} = \frac{i R_{3}}{R_{2} + R_{3}} = \frac{i}{3}$
Hence ratio of heat dissipated in the resistors= $\frac{i^{2} R_{1}}{(\frac{i}{3})^{2} R_{2}}$
$= 9 : 1$

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