Question

A copper wire of resistance R is uniformly stretched till its length is increased to n times its

original length. What will be its new resistance? Find % change in its resistance also.

Answer 1

we know,
R =pL/A
where,
R = resistance
p = resistivity
L = length of conductor
A = cross section area .

if wire stretched it means volume of wire remains constant .
hence,
R = pL²/AL
AL = volume of wire .

R directly proportional to square of length .

now, wire stretched n times
then,
R1/R2 = L²/(nL)²
R/R2 = 1/n²
R2 = R/n²

change in resistance = (final resistance - initial resistance ) = (R/n² - R)
= (1 - n²)R/n²

% change in resistance = (1 - n²)R/n²R × 100 = ( 1 - n²)× 100/n² %