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 $
