JEE Main On 08 April 2018 Question 26

Question: On interchanging the resistances, the balance point of a meter bridge shifts to the left by 10 cm. The resistance of their series combination is $ \text{1 k}\Omega $ . How much was the resistance on the left slot before interchanging the resistances? [JEE Main Online 08-04-2018]

Options:

A) $ \text{550 }\Omega $

B) $ \text{910 }\Omega $

C) $ \text{990 }\Omega $

D) $ \text{505 }\Omega $

Show Answer

Answer:

Correct Answer: A

Solution:

  • $ x+y=1000 $ $ \frac{x}{y}=\frac{\ell }{100-\ell } $ $ \frac{y}{x}=\frac{\ell -10}{110-\ell } $ $ \frac{\ell (\ell -10)}{(100-\ell )(110-\ell )}=1 $ $ {{\ell }^{2}}-10\ell =11000-100\ell -110\ell +{{\ell }^{2}} $ $ 200\ell =11000 $ $ \ell =55 $ $ \frac{x}{y}=\frac{55}{45} $ $ x=550\Omega $