First slide

combination of resistance

Question

The ring shown in fig. has zero resistance. The
equivalent resistance between points A and B will be

Easy

A

R
B

2 R
C

3R
D

4R

Solution

The three resistances of 6 R resistance each are connected in parallel. Their equivalent resistance is
$\frac{1}{R^{'}} = \frac{1}{6 R} + \frac{1}{6 R} + \frac{1}{6 R} = \frac{3}{6 R} or R^{'} = 2 R$
This R is in series with 2 R resistance. Hence, equivalent resistance between B and A will be
$R_{AB} = 2 R + 2 R = 4 R$

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