Question

$A$ resistance of 2 $\Omega$ is connected across one gap of a metre-bridge (the length of the wire is 100 cm) and an unknown resistance, greater than $2\Omega$, is connected across the other gap. When these resistance are interchanged, the balance point shifts by 20 cm. Neglecting any corrections, the unknown resistance is

• A. 3 $\Omega$
• B. 4 $\Omega$
• C. 5 $\Omega$
• D. 6 $\Omega$

Answer 1

The correct option is A 3 $\Omega$

For null condition in first case, $\frac{2}{x}=\frac{l}{100-l}$ or $lx=200-2l.....\left(1\right)$

and for second case , $\frac{x}{2}=\frac{l+20}{100-(l+20)}$

or $\frac{x}{2}=\frac{l+20}{80-l}$

or $80x-lx=2l+40.....\left(2\right)$

from (1) and (2) $\Rightarrow 80x-200+2l=2l+40$ or $80x=240$

$\therefore x=3\Omega$