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 resistances are interchanged, the balance point shifts by 20 cm . Neglecting any corrections, the unknown resistance is:

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

Answer 1

The correct option is C 5 $\Omega$

Case 1 :- Without interchanging

$\Rightarrow \frac{2}{R}=\frac{l}{100-l}$

$\Rightarrow R=\frac{2(100-l)}{l}-\left(1\right)$

Case 2 :- After interchanging

$\frac{R}{2}=\frac{l+20}{100-(20+l)}$ - (2)

$\Rightarrow$ Equating R from (1) and (2)

we get L $=$ 40 cm

$\Rightarrow R=\frac{2(100-40)}{40}$

$=\frac{2\times 60}{40}cm$

$\Rightarrow R=3\Omega$