Question

Copper and Carbon wires are connected in series and the combined resistor is kept at $0^{\circ }C$. Assuming the combined resistance does not vary with temperature, the ratio of the resistances of Carbon and Copper wires at $0^{\circ }C$ is:
(Temperature coefficients of resistivity of Copper and Carbon respectively are $4\times {10}^{-3}/{}^{\circ }C$ and $-0.5\times {10}^{-3}/{}^{\circ }C$)

• A. $8$
• B. $6$
• C. $2$
• D. $4$

Answer 1

The correct option is A $8$

It is given that combined series resistance does not change with temperature.

Thus, $R_{Cu}+R_C=R_{Cu}(1+{\alpha }_{Cu}\Delta T)+R_C(1+{\alpha }_C\Delta T)$

for all values of $\Delta T$

Thus, $R_{Cu}{\alpha }_{Cu}=-R_C{\alpha }_C$

$⟹\frac{R_C}{R_{Cu}}=-\frac{{\alpha }_{Cu}}{{\alpha }_C}$

$=-\frac{4\times {10}^{-3}}{-0.5\times {10}^{-3}}=8$