In a meter bridge experiment to determine the value of unknown resistance, first the resistances $$2\Omega$$ and $$3\Omega$$ are connected in the left and right gaps of the bridge and the null point is obtained at a distance l cm from the left. Now when an unknown resistance $$x\Omega$$ is connected in parallel to $$3\Omega$$ resistance, the null point is shifted by 10 cm to the right of wire. The value of unknown resistance x is __________ $$\Omega$$ .

We need to find the unknown resistance x connected in parallel with 3Ω in a meter bridge.

Initially, 2Ω is on the left and 3Ω is on the right, and the null point is at a distance l from the left.

$$\frac{2}{3} = \frac{l}{100-l} \implies l = 40 \text{ cm}$$

When x is connected in parallel with the 3Ω resistor, the effective resistance on the right becomes $$R_{eff} = \frac{3x}{3+x}$$.

The null point shifts 10 cm to the right, so the new null point is at $$l' = 50$$ cm.

$$\frac{2}{\frac{3x}{3+x}} = \frac{50}{50} = 1$$

$$\frac{2(3+x)}{3x} = 1$$

$$6 + 2x = 3x$$

$$x = 6 \, \Omega$$

Therefore, x = 6 Ω.