Question

In the adjoining circuit, the resistances are given in ohm, and \(X\) and \(Y\) are unknown resistances. The current through the 10 \(\Omega\) resistance is 3A while that through the resistance \(X\) is 1A. No current passes through the galvanometer. The values of the unknown resistances \(X\) and \(Y\) are respectively}

• A. 12 \(\Omega\) and 12 \(\Omega\)
• B. 12 \(\Omega\) and 6 \(\Omega\)
• C. 6 \(\Omega\) and 12 \(\Omega\)
• D. 6 \(\Omega\) and 6 \(\Omega\)

Hint:

When galvanometer reads zero (balanced bridge): \(\dfrac{R_1}{R_2} = \dfrac{R_3}{R_4}\). Apply KVL/KCL to find unknown resistances.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
When no current passes through the galvanometer (Wheatstone bridge balanced): \(\dfrac{P}{Q} = \dfrac{R}{S}\). Also apply KCL at junctions.
Step 2: Detailed Explanation:
From the circuit: Current through 10 \(\Omega\) = 3 A; through \(X\) = 1 A.
Using Kirchhoff's laws and bridge balance condition with given resistances (24 \(\Omega\), 84 \(\Omega\), 30 \(\Omega\), 10 \(\Omega\), \(X\), \(Y\)):
By voltage division and Wheatstone balance: \(X = 6\ \Omega\), \(Y = 12\ \Omega\).
Step 3: Final Answer:
\(X = \mathbf{6\ \Omega}\) and \(Y = \mathbf{12\ \Omega}\).