question_answer

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]

A) \[\text{550 }\Omega \]

B) \[\text{910 }\Omega \]

C) \[\text{990 }\Omega \]

D) \[\text{505 }\Omega \]

Correct Answer: A

Solution :

[a]

\[x+y=1000\]

\[\frac{x}{y}=\frac{\ell }{100-\ell }\]

\[\frac{y}{x}=\frac{\ell -10}{110-\ell }\]

\[\frac{\ell (\ell -10)}{(100-\ell )(110-\ell )}=1\]

\[{{\ell }^{2}}-10\ell =11000-100\ell -110\ell +{{\ell }^{2}}\]

\[200\ell =11000\]

\[\ell =55\]

\[\frac{x}{y}=\frac{55}{45}\]

\[x=550\,\,\Omega \]