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

Option 1 - <math> <mn>1.8</mn> <mi> </mi> <mi>m</mi> <mi> </mi> </math>

Option 2 - <math> <mn>2</mn> <mi> </mi> <mi>m</mi> <mi> </mi> </math>

Option 3 - <math> <mn>3.6</mn> <mi> </mi> <mi> </mi> <mi>m</mi> </math>

Option 4 - <math> <mn>4</mn> <mi> </mi> <mi>m</mi> <mi> </mi> </math>

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Alok Kumar Singh | Contributor-Level 10

4 months ago

Correct Option - 2

Detailed Solution:

Resistance of whole wire is

$R = r^{'} * l$

$20 = 1 * l$

$l = 20 m$

Let length of the shorter section = a

$\frac{1}{R} = \frac{1}{a} + \frac{1}{(20 - a)}$

$\frac{1}{1.8} = \frac{20 - a + a}{a (20 - a)} ? 20 a - a^{2} = 36$

$a = 2 a n d 18$

$? a = 2 m$

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

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