Browse Questions

# Two conductors have the same resistance at $0^{\circ}C$ but their temperature coefficient of resistance are $\alpha 1\: and \: \alpha 2$. The temperature coefficient for the series combination is

$\begin {array} {1 1} (A)\;\alpha_1 + \alpha_2 & \quad (B)\;\large\frac{(\alpha_1+ \alpha_2)}{2} \\ (C)\;\large\frac{(\alpha_1\alpha_2)}{(\alpha_1+ \alpha_2)} & \quad (D)\;\large\frac{2(\alpha_1 \alpha_2)}{(\alpha_1+ \alpha_2)} \end {array}$

$R_s = R + R = 2R$
$R_s(1 + \alpha_s \theta) = R(1 + \alpha_1 \theta ) + R(1 + \alpha_2 \theta)$
$\Rightarrow \alpha_s = \large\frac{(\alpha_1 + \alpha_2)}{2}$
Ans : (B)

edited Sep 3, 2014