Question

The Wheatstone bridge is an arrangement of four resistances, say \(R_1, R_2, R_3\), and  \(R_4\). The null point condition is given by:

• A. \(\quad \frac{R_1}{R_2} = \frac{R_3}{R_4} \\\)
• B. \(\quad R_1 + R_2 = R_3 + R_4 \\\)
• C. \(\quad R_1 - R_2 = R_2 - R_4 \\\)
• D. \(\quad R_1 \times R_2 = R_3 \times R_4\)

Answer 1

The Correct Option is A

Four resistances arranged in a Wheatstone bridge configuration: \( R_1 \), \( R_2 \), \( R_3 \), \( R_4 \)

Null Point Condition:

The bridge is balanced when the potential difference between the midpoints is zero, which occurs when:

\[ \frac{R_1}{R_2} = \frac{R_3}{R_4} \]

This means the ratio of resistances in one arm equals the ratio in the opposite arm.

Option Analysis:

1. Correct: \( \frac{R_1}{R_2} = \frac{R_3}{R_4} \) is the standard balance condition
2. Incorrect: Sum of resistances doesn't determine balance
3. Incorrect: Difference of resistances is irrelevant
4. Incorrect: Product of resistances doesn't determine balance

Answer 2

The Wheatstone bridge is balanced when the ratio of the two resistances in one branch equals the ratio of the two resistances in the other branch:
\(\quad \frac{R_1}{R_2} = \frac{R_3}{R_4} \\\)This is the condition for zero current through the galvanometer.