A wire of resistance 20 Ω is bent in form of a closed circle. What is the effective resistance between two points at the ends of any diameter of the circuit?
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Since it is a wire of uniform resistance, let's say the length is l and so resistance per unit is 20/l. Now when it is bent into a circle and the resistance is to be calculated between two ends of the diameter, it resembles a situation of two resistances in parallel. Now we have to find the value of each resistor. Each part is now l/2 length, and so it's resistance is l/2 *20/l which is 10 ohm. So, now the situation is of two 10 ohm resistances in parallel connection which can be resolved by Req = R1R2/(R1+R2) = 5 ohms.
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Since it is a wire of uniform resistance, let's say the length is I and so resistance per unit is 20/1. Now when it is bent into a circle and the istance is to be calculated between two ends of the diameter, it resembles a situation of two resistances in parallel. Now we have to find the value of each resistor. Each part is now 1/2 length, and so it's resistance is 1/2 *20/1 which is 10 ohm. So, now the situation is of two 10 ohm resistances in parallel connection which can be resolved by Req = R1R2/(R1+R2) = 5 ohms.
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