Answer to Question #113514 in Electric Circuits for Peter

Question

11. The temperature coefficient of resistance for carbon at 0oC is
-0.0048/oC. What is the significance of the minus sign?
A carbon resistor has a resistance of 500Ω.Determine its resistance at 50oC

Answer 1

1. The significance of the minus sign is the following: resistance of carbon decreases with increasing temperature, as one can conclude from the following formula:

$R(T) = R(T_0)(1 + \alpha\Delta T)$ ,

where $R(T)$ is the resistence at temperature T, $R(T_0)$ is the resistance at temperature $T_0$ (in our case $T_0=0\degree C$ ), $\Delta T =T-T_0$ and $\alpha$ is the temperature coefficient of resistance.

2. From the previous equation:

$R(T) = 500\Omega(1 -0.0048\frac{1}{\degree C}(50\degree C-0\degree C)) = 380\Omega$.