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:
A Wheatstone bridge is balanced when the ratio of resistances in adjacent arms is equal: $\frac{P}{Q} = \frac{R}{S}$.
Step 2: Formula Application:
Assuming the order given is $P=2, Q=6, R=X, S=12$: $$\frac{2}{6} = \frac{X}{12}$$
Step 3: Explanation:
$\frac{1}{3} = \frac{X}{12}$ $3X = 12 \implies X = 4$ $\Omega$.
Step 4: Final Answer:
The value of X is 4 $\Omega$.