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 $1k\Omega$. How much was the resistance on the left slot before interchanging the resistances?

• A. $550\Omega$
• B. $910\Omega$
• C. $990\Omega$
• D. $505\Omega$

Answer 1

The correct option is A $550\Omega$

Let the resistance in the left slot be $R_1$ and position of balance point $l_1$.
Resistance in right box $R_2=1000-R_1$
Its corresponding balance point $l_2=100-l_1$
Using balanced wheat stone bridge equation, $\frac{R_1}{R_2}=\frac{l_1}{100-l_2}$ ........(1)
Given : $l_1-l_2=10cm$
$\therefore$ $l_1-(100-l_1)=10$
$⟹$ $l_1=55cm$
From (1), $\frac{R_1}{1000-R_1}=\frac{55}{100-45}$
$⟹R_1=550\Omega$