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?
- A.2 ohm
- B.10 ohm
- C.0.5 ohm
- D.5 ohm
Correct answer
Explanation
The correct answer is A, 2 ohm. Each piece has a resistance of 10 ohm, and five equal 10-ohm resistors in parallel give 10 ÷ 5 = 2 ohm.
The resistance of a wire is proportional to its length (R = ρL/A). Cutting the 50-ohm wire into five equal lengths gives five wires of 10 ohm each. In parallel, the reciprocals add: 1/R = 1/10 + 1/10 + 1/10 + 1/10 + 1/10 = 5/10, so R = 2 ohm. A quick rule is that n equal pieces of a wire of resistance R, joined in parallel, give R/n².
B is wrong: 10 ohm is the resistance of one piece, not of the parallel combination.
C is wrong: 0.5 ohm would need far more pieces; it does not follow from five 10-ohm wires.
D is wrong: 5 ohm would result from only two 10-ohm wires in parallel.
Exam tip: cut a wire into n equal parts and join them in parallel, and the resistance becomes R/n²; 50/25 = 2 ohm.
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