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Question

The three resistances of equal values are arranged in different combinations shown. Arrange them in increasing order of power dissipation.
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A
III < II < IV < I
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B
II < III < IV < I
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C
I < IV < III < II
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D
I < III < II < IV
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Solution

The correct option is A III < II < IV < I
For (I) : $$R_{eq}=R+R+R=3R$$ and Power dissipation, $$P_{I}=i^2R_{eq}=i^2(3R)$$
For (II): $$R_{eq}=\dfrac{(R+R)R}{(R+R)+R}=(2/3)R$$ and Power dissipation, $$P_{II}=i^2R_{eq}=i^2(2R/3)$$
For (III): $$R_{eq}=(1/R+1/R+1/R)^{-1}=R/3$$ and Power dissipation, $$P_{III}=i^2R_{eq}=i^2(R/3)$$
For (IV): $$R_{eq}=\dfrac{RR}{R+R}+R=(3/2)R$$ and Power dissipation, $$P_{IV}=i^2R_{eq}=i^2(3R/2)$$
Thus, $$ III<II<IV<I$$

Physics

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