In an electric circuit, a wire of resistance 10 Ω is used. If this wire is stretched to a length double of its original value, the current in the circuit would become :
- A.half of its original value.
- B.double of its original value.
- C.one-fourth of its original value.
- D.four times of its original value.
Correct answer
Explanation
The correct answer is C, one-fourth of its original value. Stretching the wire to twice its length makes its resistance four times larger, so at the same voltage the current falls to a quarter.
The resistance of a wire is R = ρL/A, where ρ is the resistivity of the material, L the length and A the area of cross-section. When a wire is stretched, its volume stays the same, so if the length doubles the cross-sectional area halves. Resistance therefore rises by a factor of 2 × 2 = 4, from 10 Ω to 40 Ω. By Ohm's law, I = V/R, so with the supply voltage unchanged the current becomes one-fourth of what it was. The resistivity does not change, since it depends only on the material and temperature.
A is wrong because it counts only the longer length and forgets the thinner wire. B and D are wrong because a higher resistance can only lower the current, never raise it.
Exam tip: stretching a wire n times its length raises its resistance n² times; resistivity stays the same.
Practice Questions
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