When a conducting wire is stretched due to a deforming force, its diameter decreases to
40% of its original value. We need to determine the percentage change in its resistance.
Conceptual Framework:
Volume Conservation:
When the wire is stretched, its volume
(V) remains constant. Therefore, the relationship between volume, cross-sectional area
(A), and length
(l) is given by:
V=A×lSolving for
l, we have:
l=Resistance Formula:
The resistance (
R ) of a wire is determined by its resistivity (
ρ ), length, and cross-sectional area:
R=ρ⋅=Given the relation between area and diameter (
D ), we express
A in terms of
D :
A=Thus, resistance can be reformulated as:
R==Change in Resistance:
The percentage change in resistance can be calculated using the change in diameter:
=−4Given the diameter decreases to
40% of its original value, the change in diameter is
∆D=−0.6D.
Substituting this into our percentage change formula, we get:
=−4(−0.6)=4×0.6=1.6%Therefore, the percentage change in resistance as a result of the stretching is
1.6%.