Answer to Question #276419 in Electric Circuits for Rex

Question

Two heating elements which is 500 ohms and 250 ohms are connected in series with temperature coefficients of 0.001 and 0.003 ohms per °C, respectively at 20°C. Calculate the effective temperature coefficient of the combination.

Answer 1

Resistance at t=0 °C

$R_0=R_T (1- α_TT) \\ R_0(500 \; \Omega) = 500(1-0.001 \times 20) = 490 \; \Omega \\ R_0(250 \; \Omega) = 250(1 -0.003 \times 20) = 235 \; \Omega \\ (490 + 235) = (500+250)(1-α_T \times 20) \\ 725 = 750(1 -20α_T) \\ 1-20α_T = 0.9667 \\ α_T = \frac{0.0333}{20} = 0.00167$