Calculate the resistance of a 1km length, 1mm diameter wire made from:

a) constantan (\rho = 4.9 × 10-7 Ωm)
b) copper (\rho = 1.7 × 10-8 Ωm)

c) State which material is better suited for being used to make resistors, and justify your answer.
d) With 1 amp of current flowing through each of the wires how much energy is converted to heat?
e) What potential difference would be needed to force a current of 1 amp through that length of each type of wire?

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pstnonsonjoku pstnonsonjoku · Answer 1 · 2021-12-31T15:40:26+01:00

From the values of resistivity, the resistance of copper wire is 22 Ω.

Let us recall that;

R = ρl/A

ρ = resistivity

l = length of the wire

A = cross sectional area of the wire

For constantan;

R = 4.9 × 10^-7 × 1 × 10^3/[3.14 × ((1 × 10^-3)/2)^2]

R = 620 Ω

For copper;

R = 1.7 × 10-8 × 1 × 10^3/[3.14 × ((1 × 10^-3)/2)^2]

R = 22 Ω

The material that is best suitable to make resistors is constantan wire.

For constantan, the energy converted to heat is;

I^2 R = (1)^2 × 620 Ω = 620 W

For copper, the energy converted to heat is;

I^2R = (1)^2 × 22 Ω = 22Ω

The potential difference of constantan = IR = 1 × 620 Ω = 620 V

The potential difference of copper = = IR = 1 × 22Ω = 22 V

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