Question

Calculate the equivalent resistance between two diametrically opposite points of a circular wire of total resistance \(12\,\Omega\).

• A. \(2\,\Omega\)
• B. \(3\,\Omega\)
• C. \(4\,\Omega\)
• D. \(6\,\Omega\)

Hint:

For circular wire resistance problems, remember that resistance is proportional to the length of the wire. Connecting diametrically opposite points divides the circle into two equal semicircles which act as parallel resistors.

Answer 1

The Correct Option is B

Concept: When a circular wire is connected between two diametrically opposite points, the wire is divided into two equal semicircles. Since resistance is proportional to length, each semicircle will have half the total resistance. These two semicircles act as two resistors connected in parallel.

Step 1: Determine the resistance of each semicircle. Total resistance of the circular wire: \[ R = 12\,\Omega \] Since the wire is divided into two equal halves, \[ R_1 = R_2 = \frac{12}{2} = 6\,\Omega \]

Step 2: Identify the circuit configuration. The two semicircular resistances connect the same two points, so they are in parallel. \[ R_{eq} = \frac{R_1R_2}{R_1 + R_2} \]

Step 3: Calculate the equivalent resistance. \[ R_{eq} = \frac{6 \times 6}{6 + 6} \] \[ R_{eq} = \frac{36}{12} \] \[ R_{eq} = 3\,\Omega \]