Answer to Question #159213 in Electric Circuits for Ali

Question

A capacitor with a value of 2uF at 25°C has a positive temperature coefficient of 50 ppm/°C. What is the capacitance value when the temperature increase to 125°C ?

Answer 1

Explanations & Calculations

• Dependence of capacitance upon the temperature is given by

$\qquad\qquad \begin{aligned} \small C &=\small C_0\big[1+(\pm\alpha) (T-T_0)\big]\\ \small C_{needed}&=\small C_{given}\big[1+(\pm\alpha)(T_{needed}-T_{given})\big] \end{aligned}$

• Using this the needed answer can be obtained.
• That ppm notation should be normalized so as to get the units only in per celsius ($^0C$ ),

$\qquad\qquad\small 50 \,ppm=50\times 10^{-6}$

• Then,

$\qquad\qquad \begin{aligned} \small C_{398}&= \small 2\mu F\big[1+(+50\times 10^{-6}\,^0C^{-1})(125-25 \,^0C)\big]\\ &= \small \bold{2.01 \mu F} \end{aligned}$

$\qquad\qquad \begin{aligned} \small \end{aligned}$