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Question

Refer to teh circuit shown. What will be the total power dissipation in the circuit if $P$ is the power dissipated in $R_{1}$ ? It is given that $R_{2} = 4 R_{1}$ and $R_{3} = 12 R_{1}$

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A

$4 P$

B

$7 P$

C

$13 P$

D

$17 P$

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Solution

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Correct option is A)

Total equivalent resistance= $\frac{R _{2} R _{3}}{R _{2} + R _{3}} + R_{1} = \frac{4 8 R _{1} ^{2}}{1 6 R _{1}} + R_{1} = 3 R_{1} + R_{1} = 4 R_{1}$
Power dissipation at $R_{1} = I^{2} R_{1} = P$
$∴$ Power dissipation in the total circuit= $I^{2} 4 R_{1}$
$= 4 I^{2} R_{1}$
$= 4 P$

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