Question

The three resistances of equal values are arranged in different combinations shown. Arrange them in increasing order of power dissipation.

• A. III < II < IV < I
• B. II < III < IV < I
• C. I < IV < III < II
• D. I < III < II < IV

Answer 1

The correct option is A III < II < IV < I

For (I) : $R_{eq}=R+R+R=3R$ and Power dissipation, $P_I=i^2{R}_{eq}=i^2\left(3R\right)$

For (II): $R_{eq}=\frac{(R+R)R}{(R+R)+R}=\left(2/3\right)R$ and Power dissipation, $P_{II}=i^2{R}_{eq}=i^2\left(2R/3\right)$

For (III): $R_{eq}=(1/R+1/R+1/R{)}^{-1}=R/3$ and Power dissipation, $P_{III}=i^2{R}_{eq}=i^2\left(R/3\right)$

For (IV): $R_{eq}=\frac{RR}{R+R}+R=\left(3/2\right)R$ and Power dissipation, $P_{IV}=i^2{R}_{eq}=i^2\left(3R/2\right)$

Thus, $III<II<IV<I$