Question

In Wheatstone bridge, 4 resistors \( P = 10 \, \Omega \), \( Q = 5 \, \Omega \), \( R = 4 \, \Omega \), \( S = 4 \, \Omega \) are connected in cyclic order. To ensure no current through galvanometer,

• A. \( P = Q \)
• B. \( P = R \)
• C. \( P = S \)
• D. \( P = Q = R = S \)

Hint:

In Wheatstone bridge, no current flows through the galvanometer when \( \frac{P}{Q} = \frac{R}{S} \).

Answer 1

The Correct Option is B

Step 1: Wheatstone Bridge Condition.
In a Wheatstone bridge, the condition for no current through the galvanometer is: \[ \frac{P}{Q} = \frac{R}{S} \] This implies \( P \times S = Q \times R \).
Step 2: Analysis of Options.
(A) Incorrect: \( P \neq Q \) from the relation.
(B) Correct: \( P = R \) satisfies the equation \( P \times S = Q \times R \).
(C) Incorrect: \( P = S \) doesn't satisfy the equation.
(D) Incorrect: \( P = Q = R = S \) is not necessary.
Step 3: Conclusion.
The correct answer is (B), \( P = R \).