Question

If the potential difference between points B and D is zero in the given circuit, the value of x is \(\frac{1}{n} \Omega\). The value n is

• A. \(2\)
• B. \(1\)
• C. \(3\)
• D. \(4\)

Hint:

Zero potential difference between B and D means the bridge ratio holds.

Answer 1

The Correct Option is A

Step 1: Potential divider
The two sides are potential dividers across the same source, so the midpoints match when the ratios of upper to lower resistance are equal.

Step 2: Compute
Left ratio $\frac23$, right ratio $\frac{1}{x+1}$. Equal when $x = \frac12$, so $n=2$. Option (A).

Final Answer:
n = 2. \[ \boxed{\text{(A)}\ 2} \]