Question #317099

A platinum coil has a resistance of 3.146ohms at 40°C and 3.767 ohms at 100°C. Find the resistance at 0°C and the temperature coefficient of resistance at 40°C

1
Expert's answer
2022-03-24T11:01:04-0400
R(t1)=R0(1+αt1)R(t2)=R0(1+αt2)R(t_1)=R_0(1+\alpha t_1)\\ R(t_2)=R_0(1+\alpha t_2)

α=R(t2)R(t1)R(t1)t2R(t2)t1\alpha=\frac{R(t_2)-R(t_1)}{R(t_1)t_2-R(t_2)t_1}

α=3.7673.1463.1461003.76740=3.788103K1\alpha=\frac{3.767-3.146}{3.146*100-3.767*40}=3.788*10^{-3}\:\rm K^{-1}

R0=R11+αt1=3.1461+3.78810340=2.732ΩR_0=\frac{R_1}{1+\alpha t_1}=\frac{3.146}{1+3.788*10^{-3}*40}=2.732\:\Omega


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