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 :

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