Answer to Question #276415 in Electric Circuits for Rex

Question

A tungsten lamp filament has a temperature of 2,050°C and a resistance of 500 Ω when taking normal working current. Calculate the resistance of the filament when it has a temperature of 25°C. Temperature coefficient at 0°C is 0.005/°C

Answer 1

Explanations & Calculations

• Use the linear relationship between the resistance and the temperature.
• Also, assume the relationship approximate the values fair even for this high temperature difference.

$\qquad\qquad \begin{aligned} \small R &=\small R_0(1+\alpha \Delta \theta)\\ \small 500&=\small R_0(1+0.005\times[2050-25])\\ \small R_0&=\small \frac{500}{11.13}\\ &=\small 44.92\,\Omega \end{aligned}$