Question

The value of unknown resistance (x) for which the potential difference between B and D will be zero in the arrangement shown, is :

• A. \( 3 \, \Omega \)
• B. \( 9 \, \Omega \)
• C. \( 6 \, \Omega \)
• D. \( 42 \, \Omega \)

Answer 1

The Correct Option is C

In the given arrangement, we observe a Wheatstone Bridge.
For the bridge to be balanced:

\[ \frac{V_{AB}}{V_{AD}} = \frac{V_{BC}}{V_{CD}}. \]

Substituting values from the circuit:

\[ \frac{12}{6 + x} = \frac{0.5}{0.5}. \]

Simplify:

\[ 12(0.5) = (6 + x)(0.5). \]

\[ 6 = 3 + 0.5x \implies x = 6 \, \Omega. \]

Final Answer: \( x = 6 \, \Omega \).