Problem

It is desired to make a

20.0\ \Omega

coil of wire which has a zero thermal 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 so chosen 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_C = -0.5 \times 10^{-3}\ \text{K}^{-1}

and

\alpha_{Fe} = 5.0 \times 10^{-3}\ \text{K}^{-1}