First slide

combination of resistance

Question

Each of the resistances in the network shown in fig
in equal to ,R. The resistance between the terminals A and B is

Moderate

A

R
B

5 R
C

3 R
D

6 R

Solution

The equivalent circuit is shown the fig.

Since the Wheatstone's bridge is balanced, therefore no current will flow through the arm KL. Equivalent resistance between AKM = R+R= 2R Equivalent resistance between ALM = R+R= 2R The two resistances are in parallel. Hence equivalent resistance between A and B is given by
$\begin{array}{l} \frac{1}{R^{'}} = \frac{1}{2 R} + \frac{1}{2 R} = \frac{2}{2 R} = \frac{1}{R} \\ R^{'} = R \end{array}$

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