Question

The Wheatstone bridge is in balanced condition in the given figure (assume branches are 2$\Omega$, 6$\Omega$, X, and 12$\Omega$ in order), then X = ______.

• A. 12 $\Omega$
• B. 4 $\Omega$
• C. 6 $\Omega$
• D. 3 $\Omega$

Hint:

If the bridge is balanced, no current flows through the \textbf{Galvanometer} ($I_g = 0$). You can essentially ignore the middle branch!

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
In a balanced Wheatstone bridge, the ratio of resistances in adjacent arms is equal: $\frac{P}{Q} = \frac{R}{S}$.
Step 2: Detailed Explanation:
Assuming the bridge layout follows the standard ratio (where $2/X = 6/12$):
$$\frac{2}{X} = \frac{6}{12}$$
$$\frac{2}{X} = \frac{1}{2}$$
$$X = 4\text{ }\Omega$$
Step 3: Final Answer:
The value of $X$ is 4 $\Omega$.