Question

Two conductors have the same resistance at 0°C but the temperature coefficients of resistance are $\alpha_1$ and $\alpha_2$. The respective temperature coefficients of their series and parallel combinations are nearly

• A. $\frac{\alpha_1 + \alpha_2}{2}$, $\alpha_1 + \alpha_2$
• B. $\alpha_1 + \alpha_2$, $\alpha_1 + \alpha_2$
• C. $\frac{\alpha_1 + \alpha_2}{3}$, $\frac{\alpha_1 + \alpha_2}{3}$
• D. $\frac{\alpha_1 + \alpha_2}{2}$, $\alpha_1 + \alpha_2$

Hint:

For series and parallel combinations, remember that the effective temperature coefficients are calculated based on the resistances of each conductor.

Answer 1

The Correct Option is D

The temperature coefficients of resistance for series and parallel combinations are based on the respective resistances and the temperature coefficients. The series combination gives a factor of $\frac{1}{2}$ for the temperature coefficient, while the parallel combination gives the sum of the coefficients.