Question

A coil of wire has a resistance of 40.1? at 28 °C and 55.9? at 49 °C. What is the temperature coefficient of resistivity?

Answer 1

Relation between temperature and resistance is given by:

R = R0*(1 + alpha*dT)

R0 = resistance at temperature 20 C

At temperature 28 C, R = 40.1 ohm

40.1 = R0*(1 + alpha*(28 - 20))

40.1 = R0*(1 + 8*alpha)

At temperature 49 C, R = 55.9 ohm

55.9 = R0*(1 + alpha*(49 - 20))

55.9 = R0*(1 + 29*alpha)

divide both equation

alpha = A = temperature coefficient

40.1/55.9 = (1 + 8*A)/(1 + 29*A)

40.1 + 40.1*29*A = 55.9 + 55.9*8*A

A = (55.9 - 40.1)/(40.1*29 - 55.9*8)

A = 0.0221 per Celcius

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