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

Answer: (C)

$6 \, \Omega$

Answer 2

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: $x = 6 \, \Omega$.