Answer to Question #187152 in Mechanics | Relativity for Henrietta Aggreh

Question

The resistance of a Thermistor at -100c is 200kilo ohms

What is the ratio of the resistance at 400c to this resistance if the material constant is 4000kelvin

Answer 1

Explanations & Calculations

• This is really straightforward because it is about applying the equation $\small R=R_0(1+\alpha\Delta\theta)$ which shows the dependence of the temperature on the resistance.
• Once you know the original/reference resistance ($\small R_0$) with the corresponding temperature ($\small T_0$: absolute zero) then you can compute the temperature change ($\small T_R-T_0$ ) up to the point of new resistance ($\small R$ ), and find the new resistance or any ratio needed.
• Here the given temperatures are above the absolute temperature hence needs calculating from that point

• Therefore,

$\qquad\qquad \begin{aligned} \small R_{100}&=\small R_0(1+4000\Delta\theta)\\ \small R_{100}&=\small R_0\bigg[1+4000K^{-1}\times\big[(-100+273)-0\big]K\bigg] \\ &=\small 692001\,R_0\\\\ \small R_{400}&=\small R_0\bigg[1+4000\times\big[(400+273)-0\big]\bigg]\\ &=\small 2692001\,R_0\\\\ \small \frac{R_{400}}{R_{100}}&=\small \frac{2692001R_0}{692001R_0}\\ &=\small \bold{3.8902} \end{aligned}$