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An electric wire of resistance 50 ohm is cut into five equal wires. Th

June 1, 2025 by rawan239

An electric wire of resistance 50 ohm is cut into five equal wires. These wires are then connected in parallel. What is the equivalent resistance of this combination?

2 ohm

10 ohm

0.5 ohm

5 ohm

This question was previously asked in

UPSC NDA-1 – 2022

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When a wire of resistance 50 ohm is cut into five equal parts, each part will have one-fifth of the original resistance. Connecting these five equal resistances in parallel results in a combined resistance calculated using the parallel resistance formula.

The resistance of a uniform wire is directly proportional to its length. So, if the wire is cut into five equal parts, the resistance of each part is R’ = R/5 = 50 ohm / 5 = 10 ohm. When n equal resistors (each of resistance r) are connected in parallel, the equivalent resistance (Req) is given by Req = r/n. In this case, r = 10 ohm and n = 5. Thus, Req = 10 ohm / 5 = 2 ohm.

Alternatively, the formula for resistors in parallel can be used: 1/Req = 1/R1 + 1/R2 + … + 1/Rn. For five equal resistances of 10 ohm in parallel: 1/Req = 1/10 + 1/10 + 1/10 + 1/10 + 1/10 = 5/10 = 1/2. Therefore, Req = 2 ohm. Connecting resistors in parallel decreases the overall resistance.

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