### JEE Main On 8 April 2017 Question 2

##### Question: A potentiometer PQ is set up to comapre two resistances as shown in the figure. The ammeter A in the circuit reads 1.0 A when two way key $ K _3 $ is open. The balance point is at a length $ l _1 $ cm from P when two way key $ K _3 $ is plugged in between 2 and 1, while the balance point is at a length $ l _2 $ cm from P when key $ K _3 $ is plugged in between 3 and 1. The ratio of the two resistance $ \frac{R _1}{R _2}, $ is found to be - [JEE Online 08-04-2017]

#### Options:

A) $ \frac{l _1}{l _1-l _2} $

B) $ \frac{l _2}{l _2-l _1} $

C) $ \frac{l _1}{l _1+l _2} $

D) $ \frac{l _1}{l _2-l _1} $

## Show Answer

#### Answer:

Correct Answer: A

#### Solution:

- When key is at point $ V _1=iR _1=xl _1 $ when key is at (3) $ V _2=i(R _1+R _2)=xl _2 $ $ \frac{R _1}{R _1+R _2}=\frac{l _1}{l _2} $ $ \frac{R _1}{R _2}=\frac{l _1}{l _2-l _1} $