Three resistors of equal value R are arranged | vedclass

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(A) Let the value of each resistor be $R$. The power dissipated in a circuit with a constant current $i$ is given by $P = i^2 R_{eq}$,where $R_{eq}$ i

Vedclass · Accepted Answer

$III < II < IV < I$

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(A) Let the value of each resistor be $R$. The power dissipated in a circuit with a constant current $i$ is given by $P = i^2 R_{eq}$,where $R_{eq}$ is the equivalent resistance.For configuration $I$ (series): $R_{eq, I} = R + R + R = 3R$.For configuration $II$ (two in series,one in parallel): $R_{eq, II} = \frac{(2R)(R)}{2R + R} = \frac{2R^2}{3R} = \frac{2}{3}R \approx 0.67R$.For configuration $III$ (all three in parallel): $R_{eq, III} = \frac{R}{3} \approx 0.33R$.For configuration $IV$ (two in parallel,one in series): $R_{eq, IV} = \frac{R}{2} + R = 1.5R$.Comparing the equivalent resistances: $R_{eq, III} (0.33R) Since $P \propto R_{eq}$,the power dissipation follows the same order: $III < II < IV < I$.

Three resistors of equal value $R$ are arranged in the different combinations shown below. Arrange them in increasing order of power dissipation.

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