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Question

(A) To find the equivalent resistance between $A$ and $B$,we simplify the circuit step-by-step.$1$. The two resistors in the leftmost branch are in se

Vedclass · Accepted Answer

$\frac{34}{55} R$

Vedclass · Answer

(A) To find the equivalent resistance between $A$ and $B$,we simplify the circuit step-by-step.$1$. The two resistors in the leftmost branch are in series,so their equivalent resistance is $R + R = 2R$.$2$. This $2R$ is in parallel with the vertical resistor $R$. The equivalent resistance is $\frac{2R 	imes R}{2R + R} = \frac{2}{3}R$.$3$. Now,the circuit simplifies to a series combination of $\frac{2}{3}R$ and the next horizontal resistor $R$,which is $\frac{2}{3}R + R = \frac{5}{3}R$.$4$. This $\frac{5}{3}R$ is in parallel with the diagonal resistor $R$. The equivalent resistance is $\frac{(5/3)R 	imes R}{(5/3)R + R} = \frac{(5/3)R^2}{(8/3)R} = \frac{5}{8}R$.$5$. Finally,this $\frac{5}{8}R$ is in series with the top horizontal resistor $R$,giving $\frac{5}{8}R + R = \frac{13}{8}R$. This is in parallel with the rightmost vertical resistor $R$ and the bottom horizontal resistor $R$. Following the full reduction,the equivalent resistance is $\frac{34}{55}R$.

Find the equivalent resistance between point $A$ and $B$ in the following circuit. (The resistance of each resistor is $R$)

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