It is desired to make a coil of wire with zero temperature coefficient of resistance

PHYSICS · Subjective · A Level · Physics · Electricity · Electricity

Problem

It is desired to make a

20.0\ \Omega

coil of wire with zero temperature coefficient of resistance. To do this, a carbon resistor of resistance

R_1

is placed in series with an iron resistor of resistance

R_2

. The proportions of iron and carbon are chosen so that

R_1+R_2=20.00\ \Omega

for all temperatures near

20^\circ\text{C}

. How large are

R_1

and

R_2

? Given

\alpha_{\mathrm{C}}=-0.5\times10^{-3}\ \text{K}^{-1}

and

\alpha_{\mathrm{Fe}}=5.0\times10^{-3}\ \text{K}^{-1}