The resistance values of the Wheatstone bridge shown are: P = 2000Ω,Q = 500Ω,R = 3000Ω. The battery voltage E = 50 V. The value of the resistance S for balanced condition is ________ Ω (Answer in integer)

The correct option is 750.

1. Understanding the Wheatstone Bridge from the Image:
The provided diagram shows a classic Wheatstone bridge circuit. The bridge is composed of four resistive arms:
- Top-left arm resistance: $P$
- Top-right arm resistance: $Q$
- Bottom-left arm resistance: $R$
- Bottom-right arm resistance: $S$ (which is adjustable, as indicated by the arrow)
A galvanometer $G$ is connected between the top and bottom junctions, and a battery source with voltage $E$ is connected across the left and right junctions.

2. Given Values:
- $P=2000\text{Ω}$
- $Q=500\text{Ω}$
- $R=3000\text{Ω}$
- Battery voltage $E=50\text{V}$

3. Balancing Condition:
The Wheatstone bridge is in a balanced condition when no current flows through the galvanometer $G$. This occurs when the potential at the top junction equals the potential at the bottom junction. The ratio of the resistances of the opposite pairs of arms must be equal, or simply the ratio of adjacent arms on one side equals the ratio of adjacent arms on the other side:

$$\frac{P}{Q}=\frac{R}{S}$$

4. Calculating the Resistance S:
Rearranging the balance equation to solve for the unknown resistance $S$:

$$S=\frac{Q\times R}{P}$$

Substituting the given values into the formula:

$$S=\frac{500\times 3000}{2000}$$

Simplifying the calculation:

$$S=\frac{1500000}{2000}=750\text{Ω}$$

Thus, the value of the resistance $S$ required to balance the Wheatstone bridge is 750 Ω.