Question

Consider copper wire with a cross-sectional area 7.85 × 10–5 m2. Caculate the required length of this wire such that it has a resistance of 0.341 Ω at a temperature of 180°C. The resistivity of copper is 1.68 × 10–8 Ω·m at 20°C and the temperature coefficient of resitivity of copper is 3.86 × 10–3 °C-1. Ingore any effects of thermal expansion on the dimensions of the wire.

Can you please also explain how to use the temperature coefficient to find the temperature at 180°C !

Answer 1

resistivity of copper at 180

rho = rho' ( 1 + (T2-T1) )

rho = 1.68*10^-8* ( 1 + 3.86*10^-3* ( 180 - 20))

rho = 2.718*10^-8 ohm m

as we know

R = rho * L/ A

0.341 = 2.718*10^-8* L / (7.85*10^-5)

L = 985 m

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