First slide

combination of resistance

Question

Find the resistance of the portion of the circuit between A and B in the circuit shown in fig
Points A and P are connected by a copper wire of negligible resistance. Similarly, Points B and Q are also connected by a copper wire of negligible resistance

Difficult

A

3R
B

R /3
C

3R/2
D

2R/3

Solution

The three resistances are connected in parallel, [fig]
Their equivalent resistance R' is given by
$\begin{aligned} \frac{1}{R^{'}} = \frac{1}{R} + \frac{1}{R} + \frac{1}{R} = \frac{3}{R} \\ R^{'} = R / 3 \end{aligned}$

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