In meter bridge experiment for measuring unknown resistance '$$S$$', the null point is obtained at a distance $$30 \text{ cm}$$ from the left side as shown at point $$D$$. If $$R$$ is $$5.6 \text{ k}\Omega$$, then the value of unknown resistance '$$S$$' will be ______ $$\Omega$$.

In a meter bridge experiment, the null point is at $$30 \text{ cm}$$ from the left side at point $$D$$, and $$R = 5.6 \text{ k}\Omega$$. We need to find the unknown resistance $$S$$.

In a meter bridge (based on the Wheatstone bridge principle), at the null point (balance point), the ratio of the two resistances equals the ratio of the two lengths of the bridge wire:

$$\frac{S}{R} = \frac{l}{100 - l}$$

where $$l = 30 \text{ cm}$$ is the distance of the null point from the left end, $$S$$ is in the left gap, and $$R$$ is in the right gap.

$$\frac{S}{R} = \frac{30}{100 - 30} = \frac{30}{70} = \frac{3}{7}$$

Given $$R = 5.6 \text{ k}\Omega = 5600 \text{ }\Omega$$:

$$S = R \times \frac{3}{7} = 5600 \times \frac{3}{7}$$

$$S = \frac{5600 \times 3}{7} = \frac{16800}{7} = 2400 \text{ }\Omega$$

The value of the unknown resistance $$S$$ is $$2400 \text{ }\Omega$$.