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(C) The power dissipated in a circuit is given by $P = I^2 R_{eq}$,where $I$ is the current and $R_{eq}$ is the equivalent resistance.For configuratio

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$(I)$ $ < $ $(IV)$ $ < $ $(III)$ $ < $ $(II)$

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(C) The power dissipated in a circuit is given by $P = I^2 R_{eq}$,where $I$ is the current and $R_{eq}$ is the equivalent resistance.For configuration $(I)$: Three resistors are in series. $R_{eq} = R + R + R = 3R$. Thus,$P_I = I^2(3R) = 3I^2R$.For configuration $(II)$: Two resistors are in parallel,and this combination is in series with the third. $R_{eq} = R/2 + R = 1.5R$. Thus,$P_{II} = I^2(1.5R) = 1.5I^2R$.For configuration $(III)$: Three resistors are in parallel. $R_{eq} = R/3$. Thus,$P_{III} = I^2(R/3) = 0.33I^2R$.For configuration $(IV)$: Two resistors are in series,and this combination is in parallel with the third. $R_{eq} = (2R \cdot R) / (2R + R) = 2R/3 \approx 0.67R$. Thus,$P_{IV} = I^2(0.67R) = 0.67I^2R$.Comparing the values: $0.33I^2R Therefore,the increasing order of power dissipation is $(III) < (IV) < (II) < (I)$.

Three resistances of equal values are arranged in four different configurations as shown below. Power dissipation in the increasing order is

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