A circular coil of single turn has a resistance of 20 Q. Which one of the following is the con-ect value for the resistance between the ends of any diameter of the coil ?

When a uniform wire with a total resistance of 20 Ω is bent into a circular coil, any diameter divides the wire into two equal semicircular arcs. Since the resistance of a conductor is directly proportional to its length [2], each semicircular half possesses exactly half of the total resistance, which is 10 Ω [2]. When measuring the resistance between the ends of a diameter, these two 10 Ω segments are connected in a parallel configuration [2]. According to the laws of parallel circuits, the reciprocal of the equivalent resistance is the sum of the reciprocals of the individual resistances [1]. For two 10 Ω resistors in parallel, the calculation is 1/R = 1/10 + 1/10 = 2/10, resulting in an equivalent resistance of 5 Ω [2]. This demonstrates that the effective resistance across the diameter of a uniform ring is always one-fourth of the total wire resistance.

Sources

1. [2] Science , class X (NCERT 2025 ed.) > Chapter 11: Electricity > What you have learnt > p. 192
2. [1] Science , class X (NCERT 2025 ed.) > Chapter 11: Electricity > Activity 11.6 > p. 186