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A circular coil of single turn has a resistance of 20 Ω. Which one of

June 1, 2025 by rawan239

A circular coil of single turn has a resistance of 20 Ω. Which one of the following is the correct value for the resistance between the ends of any diameter of the coil?

5 Ω

10 Ω

20 Ω

40 Ω

This question was previously asked in

UPSC NDA-1 – 2017

Download PDF Attempt Online

The correct answer is 5 Ω. When a circular coil of uniform resistance is connected across a diameter, the coil is divided into two equal semicircles. These two semicircular wires act as two resistors connected in parallel between the points where the diameter touches the circle.

Let the total resistance of the circular coil be R. The resistance of each semicircle is R/2. When these two semicircles are connected in parallel, the equivalent resistance (R_eq) is given by the formula for resistors in parallel: 1/R_eq = 1/R₁ + 1/R₂. Here, R₁ = R₂ = R/2.
So, 1/R_eq = 1/(R/2) + 1/(R/2) = 2/R + 2/R = 4/R.
Therefore, R_eq = R/4.

Given the total resistance of the coil is 20 Ω. Using the formula R_eq = R/4, the equivalent resistance between the ends of any diameter is 20 Ω / 4 = 5 Ω. This method is applicable for any uniform wire bent into a circle. The connection across a diameter always results in an equivalent resistance that is one-fourth of the total resistance of the circular wire.

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