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>

5 Views|Posted 4 months ago

Asked by Shiksha User

1 Answer

Sort by:

Answered by

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

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

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

$a = 2 a n d 18$

$? a = 2 m$

Upvote

Taking an Exam? Selecting a College?

Get authentic answers from experts, students and alumni that you won't find anywhere else.

On Shiksha, get access to

66K

Colleges

1.2K

Exams

6.9L

Reviews

1.8M

Answers

Learn more about...

Physics Current Electricity 2025

View Exam Details

Share Your College Life Experience

Didn't find the answer you were looking for?

Search from Shiksha's 1 lakh+ Topics

Ask Current Students, Alumni & our Experts

Quick Actions

Community GuidelinesUser Points System

QuestionsDiscussionsTags

Have a question related to your career & education?

See what others like you are asking & answering

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

Similar Questions for you