Answer to Question #196330 in Electric Circuits for SJP

Question

If two coils are connected in series and have resistance of 400 ohms and 200 ohms with temperature coeffetients of 0.1% and 0.4% respectively at 20 degrees Celsius. What is the temperature coefficient of the combination, and what is the resistance of the combination at 50 degrees Celsius?

Answer 1

Resistance, $R_1=400\space\Omega$

$\alpha_1=0.001$

Resistance, $R_2=200\space\Omega$

$\alpha_2=0.004$

Equivalent Resistance, $R_{eq}=R_1+R_2=600\space \Omega$

Initial temperature, $T_1=20\degree C$

Final temperature, $T_2=50\degree C$

$\Delta T=30\degree C$

temperature coefficient of the combination,

$\alpha=\dfrac{R_1\alpha_1+R_2\alpha_2}{R_1+R_2}=0.002$

resistance of the combination at 50 degrees Celsius,

$R_f=R_{eq}(1+\alpha\Delta T)$

$R_f=646\space\Omega$