Question

A Wheatstone bridge is used to determine the value of unknown resistance X by adjusting the variable resistance Y as shown in the figure. For the most precise measurement of X, the resistances P and Q:

• A. Should be approximately equal to 2X
• B. Should be approximately equal and are small
• C. Should be very large and unequal
• D. Do not play any significant role

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
A Wheatstone bridge is an electrical circuit used to measure an unknown electrical resistance by balancing two legs of a bridge circuit.
The measurement is most precise when the bridge is at its highest sensitivity.
Step 2: Detailed Explanation:
1. Sensitivity: The sensitivity of the bridge refers to the deflection in the galvanometer for a small change in the unknown resistance.
2. Condition for Maximum Sensitivity: A Wheatstone bridge is most sensitive when all four resistances (\(P, Q, X, Y\)) in the arms of the bridge are of the same order of magnitude.
3. Internal Resistance and Heat: If the resistances \(P\) and \(Q\) are very large, the current through the bridge becomes very low, making it difficult for the galvanometer to detect the null point accurately.
4. Error Minimization: When \(P\) and \(Q\) are approximately equal and small, the bridge provides a sharp null point and minimizes the effects of external factors like lead resistance or thermal EMFs.
Therefore, for the most precise measurement, \(P\) and \(Q\) should be small and approximately equal to the resistances being measured.
Step 3: Final Answer:
The resistances \(P\) and \(Q\) should be approximately equal and are small.