Resistors R, 2R, 4R, 8R, ..... infty are conn | vedclass

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(B) For resistors connected in parallel,the equivalent resistance $R_{eq}$ is given by:$\frac{1}{R_{eq}} = \frac{1}{R} + \frac{1}{2R} + \frac{1}{4R} +

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$R/2$

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(B) For resistors connected in parallel,the equivalent resistance $R_{eq}$ is given by:$\frac{1}{R_{eq}} = \frac{1}{R} + \frac{1}{2R} + \frac{1}{4R} + \frac{1}{8R} + ..... \infty$Taking $\frac{1}{R}$ as a common factor:$\frac{1}{R_{eq}} = \frac{1}{R} [1 + \frac{1}{2} + \frac{1}{4} + \frac{1}{8} + ..... \infty]$The term inside the bracket is an infinite geometric series with first term $a = 1$ and common ratio $r = 1/2$. The sum $S$ of an infinite geometric series is given by $S = \frac{a}{1 - r}$.$S = \frac{1}{1 - 1/2} = \frac{1}{1/2} = 2$Substituting this back into the equation:$\frac{1}{R_{eq}} = \frac{1}{R} 	imes 2 = \frac{2}{R}$Therefore,$R_{eq} = \frac{R}{2}$.

Resistors $R, 2R, 4R, 8R, ..... \infty$ are connected in parallel. What is their equivalent resistance?

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