Question

A copper wire is stretched so that its length increases and its diameter decreases. As a result, a) both the wire resistance and resistivity increase. b) the wire resistance increases but its resistivity stays the same. c) the wire resistance increases and its resistivity decreases. d) the wire resistance decreases but its resistivity stays the same. e) both the wire resistance and resistivity decrease.

Answer 1

The correct answer is (b) the wire resistance increases but its resistivity stays the same.

Step-by-step explanation:

The electrical resistance of a wire is given by the formula R = (ρL)/A,

(where R is resistance,

ρ is resistivity,

L is length,

A is the cross-sectional area of the wire)

When we stretched the copper wire so that its length increases and its diameter decreases, both the length and area of the cross-section of the wire changes. The length increases, which means the resistance will increase. The cross-sectional area decreases, which means the resistance will also increase.

Since the resistivity of copper is a constant that depends on the material, it will not change as a result of stretching the wire. Therefore, the correct answer is (b) the wire resistance increases but its resistivity stays the same.

Answer 2

C. The wire resistance increases and its resistivity decreases. When a copper wire is stretched so that its length increases and its diameter decreases, the increase in length makes the wire more resistant to electrical current. Since resistivity takes into account the wire's cross-sectional area, the decrease in diameter causes its resistivity to decrease as well.