Question

A wire is stretched to increase its length by 5% calculate percentage change in its resistance

Answer 1

Answer:

10.25 %

Explanation:

A wire is stretched to increase its length by 5% calculate percentage change in its resistance

Let say Resistance of Wire = R

Length = L

Area = A

Resistivity = ρ

R = ρL/A

Volume = V = LA

wire is stretched to increase its length by 5%

New L = L + (5/100)L = 1.05L

Volume remains same

so new Area = V/1.05L  = A/1.05

New resistance = ρ 1.05L /(A/1.05)

New R = (ρL/A) * (1.05)²

New R = R * 1.05²

increase in R  = R * 1.05² - R   = R ( 1.05 + 1)(1.05 - 1)  = R(2.05)(0.05)

% increase in R = (R(2.05)(0.5)/R ) * 100   = 2.05 * 5 = 10.25 %

10.25 % increase in resistance