Question

a copper wire has cross sectional area of 4*10^-8 ohm meter. Calculate its length to make its resistance 10 ohm. How much does R change if the diameter of the wire is doubled?

Answer 1

Wire A.

Length = l.

Radius =r.

Area =pie r2.

R1= rho x l /pie r2.

Wire B.

Length = 2l.

Radius = 2r.

Area = pie 4r2.

R2= rho x 2l/pie 4r2=rho x l /pie x 2r2.

total resistance.

1/Rp= 1/R1+1/R2.= pie r2/rho x l+2 pie r2/ rho x l.=3 pie r2/rho x l.

Rp= rho x l/ 3 pie x r2.

ratio = Rp/ R1= rho /3 pie r2divided by rho x l / pie x r2.

Rp / R1= 1 : 3.

Hope it helps you.

Answer 2

Answer:

Given,

R= 10Ω

A= 10×10 ^−8 m ^2

ρ=1.6×10 ^−8Ω/m

We know that,

R =ρ A/l

l= RA/ρ

10×10×10 ^−8

=___________

1.6×10 ^−8

l =62.5m

The length of wire copper wire is 62.5m.