Question

A wire of length L and resistance R is stretched so that the length is doubled and area of cross section halved. How will its (I) resistance change ? (II) resistivity change ? (Include necessary steps/reasons to support your answer)

Answer 1

(a) Here, length is doubled and area of cross-section is halved. Thus, a wire of length $l$ and area of cross-section $A$ becomes a wire of length $2l$ and area of cross-section $\frac{A}{2}$.

Using $R=\rho \frac{l}{A}$

New resistance, $R_{1=\rho \frac{2l}{A/2}}$

$R_{1=\frac{4\rho l}{A}=4xR}$

i.e., resistance becomes four times.

(b) Resistivity of a substance does not depend on its length or area of cross-section. It depends on the nature of the material and temperature. Hence there is no change.