Natural response RC circuit

rc circuit

the simplest rc circuit capacitor , resistor in series. when circuit consists of charged capacitor , resistor, capacitor discharge stored energy through resistor. voltage across capacitor, time dependent, can found using kirchhoff s current law, current charging capacitor must equal current through resistor. results in linear differential equation

c



d
v


d
t



+


v
r


=
0

,


{\displaystyle c{\frac {dv}{dt}}+{\frac {v}{r}}=0\,,}

where c capacitance of capacitor.

solving equation v yields formula exponential decay:

v
(
t
)
=

v

0



e

−


t

r
c






,


{\displaystyle v(t)=v_{0}e^{-{\frac {t}{rc}}}\,,}

where v0 capacitor voltage @ time t = 0.

the time required voltage fall v0/e called rc time constant , given by

τ
=
r
c

.


{\displaystyle \tau =rc\,.}






^ horowitz , hill: art of electronics