Wheaststone bridge is most sensitive when the resistance of all four arms are

Options

A. greater than `10 Omega`
B. less than 10 `Omega`
C. same
D. none of the above

Explanation

To determine when a Wheatstone bridge is most sensitive, we need to analyze the conditions under which it operates. Here’s a step-by-step solution:

### Step-by-Step Solution:

1. **Understanding Wheatstone Bridge**:
A Wheatstone bridge consists of four resistors arranged in a diamond shape, with a voltage source connected across one diagonal and a galvanometer connected across the other diagonal. The resistors are typically labeled as R1, R2, R3, and R4.

2. **Condition for Balance**:
The bridge is said to be balanced when the ratio of the resistances in one arm is equal to the ratio in the other arm. Mathematically, this is expressed as:
\[ \frac{R1}{R2} = \frac{R3}{R4} \]
When the bridge is balanced, the current through the galvanometer is zero.

3. **Sensitivity of the Bridge**:
The sensitivity of the Wheatstone bridge refers to its ability to detect small changes in resistance. The sensitivity is highest when the bridge is balanced, and small changes in resistance can cause a significant deflection in the galvanometer.

4. **Equal Resistance Condition**:
The Wheatstone bridge is most sensitive when all four resistances are equal, i.e., \( R1 = R2 = R3 = R4 \). This condition maximizes the change in current through the galvanometer for a given change in resistance.

5. **Conclusion**:
Therefore, the Wheatstone bridge is most sensitive when the resistance of all four arms are equal.

### Final Answer:
The Wheatstone bridge is most sensitive when the resistance of all four arms are equal.

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