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 ?
- A.5 Ω
- B.10 Ω
- C.20 Ω
- D.40 Ω
Correct answer
Explanation
The correct answer is A, 5 Ω. The two ends of a diameter split the ring into two equal halves of 10 Ω each, and these two halves are connected in parallel.
Resistance of a uniform wire is proportional to its length, so each semicircle has half the total resistance, 20 ÷ 2 = 10 Ω. Between the ends of the diameter, current can flow along either half, so the halves are in parallel. For two equal resistors R in parallel the combined value is R/2, giving 10 ÷ 2 = 5 Ω. The general rule is 1/R = 1/R₁ + 1/R₂, and a parallel combination is always smaller than its smallest branch.
B is wrong because 10 Ω is the resistance of one half alone, ignoring the second path. C is wrong because 20 Ω is the resistance of the whole wire end to end. D is wrong because 40 Ω would mean adding resistances in series, which is not how the halves are joined.
Exam tip: a ring of resistance R measured across a diameter gives R/4; across any two points splitting it into r₁ and r₂, use r₁r₂/(r₁ + r₂).
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