A copper wire has length Land cross-sectional area A. Its resistance is R. If we halved the length and halved the diameter of the wire, then what will be the resistance of this wire?
Correct answer: C. 2R
- A. 4R
- B. 3R
- C. 2R
- D. R
Explanation
The resistance of a wire is given by R∝L/A, and the cross-sectional area is proportional to the square of the diameter, A∝d². If the length of the wire is halved (L′=L/2), the resistance becomes half. If the diameter is also halved (d′=d/2), the area becomes one-quarter (A′=A/4), which increases the resistance four times. Considering both changes together, the new resistance is R′=R×1/2×4=2R.
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