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 -

$1.8 m$

Option 2 -

$2 m$

Option 3 -

$3.6 m$

Option 4 -

$4 m$

2 Views | Posted 2 weeks ago

Asked by Shiksha User

1 Answer

Answered by

alok kumar singh | Contributor-Level 10

2 weeks ago

Correct Option - 2

Detailed Solution:

Resistance of whole wire is

$R = r^{'} \times l$

$20 = 1 \times l$

$l = 20 m$

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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