# 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?

By BYJU'S Exam Prep

Updated on: September 25th, 2023

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

Summary:-

## 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?

Given that 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. Therefore the resistance change if the diameter is doubled is 2.5 Ω

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