Answer to Question #204167 in Electric Circuits for Daryll

Question

1.    A length of copper wire (α = 0.004041 at 20^o C) has a resistance of 5 ohms at 20 degrees Celsius. Calculate its resistance if the temperature were to increase to 50 degrees Celsius. 

Answer 1

Explanations & calculations

• The available data are

$\qquad\qquad \begin{aligned} \small R_0 &=\small 5\Omega\\ \small T_0 &=\small 20C^0\\ \small T_1 &=\small 50C^0 \end{aligned}$

• Then simply using the equation for the temperature dependence of resistance, we can calculate the new resistance.
• The resistance of conductors increases as the temperature rises. Note the thermal coefficient of resistance is positive.
• Then substituting the values,

$\qquad\qquad \begin{aligned} \small R_{1}&=\small R_0(1+\alpha\Delta\theta)\\ &=\small 5(1+0.004041C^{-1}\times[50-20]C)\\ &=\small \bold{5.606\,\Omega} \end{aligned}$