First slide

combination of resistance

Question

A uniform wire of resistance 20 ohm having resistance 1 $Ω$ /m is bent in form of a circle as shown in fig. If the equivalent resistance between M and N is 1.8 $Ω$ , then the length of the shorter section is

Moderate

A

2m
B

5m
C

1.8 m
D

18 m

Solution

Let the resistance of the shorter part MN be x. Total resistance is 20. Hence the resistance of longer MN part will be (20 -x). With respect to M and N, the portions are connected in parallel. Hence
$∴ R_{eq} = \frac{(20 - x) \times x}{(20 - x) + x} = 1 \cdot 8$
Solving, we get x = 2m
The resistance is 1 $Ω$ / m and hence the length of shorter part MN
= 2 x 1= 2m

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