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A wire in a circular shape has 10 Ω resistance. The resistance of the wire per 1 m length is 1 Ω. If the equivalent resistance between A and B is 2.4 Ω, then the length of the shorter arc AB will be equal to ______ metre.

Asked in RS Academy GUJCET booklet · Wires bent into shapes

Answer: (2) 4

Step-by-step solution

Given: the whole ring is 10 Ω at 1 Ω m⁻¹, so its circumference is 10 m.

Idea: A and B split the ring into two arcs, and these two arcs are in parallel between A and B.

Let one arc have resistance x; the other then has 10-x.

(x(10-x))/(10)=2.4, so x²-10x+24=0.

(x-4)(x-6)=0: the arcs are 4 Ω and 6 Ω, that is 4 m and 6 m of wire.

The shorter arc AB is 4 m long.

Why the other options are wrong

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