The length of a certain wire is doubled while its radius is kept constant. What is the new resistance of this wire?
A) It is 3 times as large.
B) It is 2 times as large.
C) It stays the same.
D) It is $1 / 2$ as large.
E) It is 4 times as large.

Question

The length of a certain wire is doubled while its radius is kept constant. What is the new resistance of this wire? 
A) It is 3 times as large.
B) It is 2 times as large.
C) It stays the same.
D) It is $1 / 2$ as large.
E) It is 4 times as large.

Quizplus · Accepted Answer

The resistance $R$ of a wire is directly proportional to its length $L$ (i.e., $R \propto L$) and inversely proportional to the cross-sectional area $A$ (i.e., $R \propto 1/A$). Since the radius is constant, the area remains the same, and only the length is doubled. Therefore, the resistance will also double.

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