Question

Two resistances equal at $0^{\circ} \, C$ with temperature coefficient of resistance $\alpha_1$ and $\alpha_2$ joined in series act as a single resistance in a circuit. The temperature coefficient of their single resistance will be

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

Answer 1

Answer: (D)

$R _{1}= R _{0}\left(1+\alpha_{1} t \right)+ R _{0}\left(1+\alpha_{2} t \right)$
$=2 R _{0}\left(1+\frac{\alpha_{1}+\alpha_{2}}{2} t \right)$
Comparing with $R=R_{0}(1+\alpha t)$
$\alpha=\frac{\alpha_{1}+\alpha_{2}}{2} .$