Question

A wire of length L and diameter D has a resistance R. If the length and the diameter of the same wire are decreased to half of their original values, the resistivity of the new wire

a. doubles.
b. drops to half its original vale.
c quadruples
d. drops to one quarter its original value.
e. remains the same.

Answer 1

e. remains the same

Step-by-step explanation:

• The resistance of a wire, depends on three parameters: the length, the circular cross-sectional area, and the resistivity.
• The resistivity -assumed the resistor is in the linear zone of operation- is constant, and depends exclusively on the material from which the wire is manufactured.
• So, if the length and the diameter are modified, the resistivity doesn't change.
• The option e) is the right one.