Jroaden

Physics graduate student at University of Kentucky in Lexington, KY.

Mathematics teacher at the Martin County ATC

Mathematics and science teacher at The Piarist School.

Here, I'm gonna play with typesetting math.

Charging capacitor:

${\displaystyle V(t)=V_{max}\left(1-e^{-t/RC}\right)}$

Discharging capacitor:

${\displaystyle V(t)=V_{max}\left(e^{-t/RC}\right)}$

When ${\displaystyle t=\tau =RC}$ ...

${\displaystyle V(\tau )=V_{max}\left(1-e^{-1}\right)\approx 0.63V_{max}}$

${\displaystyle V(\tau )=V_{max}\left(e^{-1}\right)\approx 0.37V_{max}}$

The quadratic equation:

${\displaystyle {\frac {-b\pm {\sqrt {b^{2}-4ac}}}{2a}}}$