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(C) For three equal resistors,each of resistance $R$,the possible combinations are:$1$. All three in series: $R_{eq} = R + R + R = 3R$$2$. All three i

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Four

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(C) For three equal resistors,each of resistance $R$,the possible combinations are:$1$. All three in series: $R_{eq} = R + R + R = 3R$$2$. All three in parallel: $\frac{1}{R_{eq}} = \frac{1}{R} + \frac{1}{R} + \frac{1}{R} = \frac{3}{R} \implies R_{eq} = \frac{R}{3}$$3$. Two in parallel,connected in series with the third: $R_{eq} = \frac{R}{2} + R = \frac{3R}{2} = 1.5R$$4$. Two in series,connected in parallel with the third: $\frac{1}{R_{eq}} = \frac{1}{2R} + \frac{1}{R} = \frac{3}{2R} \implies R_{eq} = \frac{2R}{3} \approx 0.67R$Thus,there are $4$ distinct ways to combine three equal resistors.

Given three equal resistors,how many different combinations of all the three resistors can be made?

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