Question

If the length of the copper wire is increased by 5%due to stretching. What will be the percentage increase in its resistance

Answer 1

Answer:

10.25%

Explanation:

A wire us stretched increase to length by 5% consider to initial length is l and cross sectional area is A

∴  volume V=Al

Now length is increased by 5%

∴  New length = 105/100=1 20/21

If new area is l considering that the volume of the wire is unchanged

V=A1=A;1 20/21

=> A=20/21A

Now if resistanty of the wire is ρ then initial Resistance

R1=ρ1/A

Final Resistance

R2=ρ*(1 20/21)/(20/21A)

=> ρ1/A(20/21)

=>

∴R2/R1=(21/20)^2

=> 441/400

% change in resistance = {(R2-R1)/R1}*100

=> 10.25%