Q 12-03-064JEE MainJEE Main 2026 (24 Jan, Shift 1)Medium
Two resistors $2\Omega$ and $3\Omega$ are connected in the gaps of bridge as shown in figure. The null point is obtained with the contact of jockey at some point on wire $XY$. When an unknown resistor is connected in parallel with $3\Omega$ resistor, the null point is shifted by 22.5 cm toward $Y$. The resistance of unknown resistor is ______ $\Omega$.
Answer: (D) 2
Initially: $\dfrac23 = \dfrac{l}{100 - l}\Rightarrow l = 40$ cm.
New null point: $40 + 22.5 = 62.5$ cm.
$$\frac{2}{R'} = \frac{62.5}{37.5} = \frac53\Rightarrow R' = 1.2\ \Omega$$
$R'$ is $3\ \Omega$ in parallel with $x$:
$$\frac{3x}{3 + x} = 1.2\Rightarrow 3x = 3.6 + 1.2x\Rightarrow x = 2\ \Omega$$
Solution by Sreeraj P, M.Sc Physics