A Copper Wire Has a Diameter of 0.5 mm and Resistivity of 1.6 X 10-8 Ωm. What Will Be the Length of This Wire to Make Its Resistance 10 Ω? How Much Does the Resistance Change if the Diameter is Doubled?

A copper wire has a diameter of 0.5mm and resistivity of 1.6 x 10^-8 Ωm. The length of this wire to make its resistance 10 Ω is 122.7 m. The resistance change if the diameter is doubled is 2.5 Ω.

Step 1:Given data

The resistivity of wire ρ = 1.6 x 10^-8 Ωm

Diameter of wire d = 0.5 mm = 5 x 10^-4 m

Let the length of the wire be l

Let the cross-sectional area of the wire be A

Resistance R = 10 Ω

Step 2: Now we have to calculate new resistance

We know that A = πd²/4

R = ρl/A

l = ρR/ πd²/4 = Rπd²/ρ4

Substituting the values we get

= [10 x 3.14 x (5 x 10^-4)²]/ [1.6 x 10^-8 x 4]

On simplifying we get

= [5 x 31.4 x 25]/ [16 x 2]

= 122.7 m

Length to make resistance as 10 Ω is 122.7 m

R ∝ 1/d²

As a result, resistance will only be one-fourth as strong when the diameter is doubled.

Hence, new resistance will be ¼ x 10 = 5/2 = 2.5 Ω