Answer to Question #167039 in Electric Circuits for Richard

Question

The temperature coefficient of resistance for carbon at 0℃ is -0.00048/℃.What is the significance of the minus sign? A carbon resistor has a resistance of 500 Ω at ℃. Determine it's resistance at 50 ℃?

Answer 1

Explanations & Calculations

• The temperature dependence of the resistance of a material is given by the equation $\small R_{\theta}=R_0(1+\alpha\Delta\theta)$
• The temperature coefficient of the resistance determines the behavior of the resistance over the temperature change.
• Therefore, negativity in that says the resistance of the material is reduced over the increment of temperature.
• This is the common behavior of the semi-conductor materials like carbon/silicon etc.
• Using the equation the needed resistance can be found

$\qquad\qquad \begin{aligned} \small R_{50}&=\small R_0(1-\alpha\Delta\theta)\\ &=\small500\Omega\big(1-0.00048C^{-1}\times[50C^0-0C^0]\big)\\ &=\small \bold{488\Omega} \end{aligned}$