# RC discharge into an LR circuit

1. Jun 27, 2012

### tml10

Hello,
I am working on a creating the characteristic equation (in general terms) of the voltage (and current, but not as important) for the capacitor in a RC connected to a LR. The RC circuit is initially charge (say has been connected to a power supply for all time before t = 0) and at t = 0 a switch is flipped and connects the RC to the RL, and allows the RC to do a DC discharge through the RL.

The circuit description in terms of nodes (pSpice convention):
C1 goes from nodes 1 to 0 (0 being ground, and C1 has an initial charge of Vi)
R1 goes from nodes 1 to 2
switch goes from nodes 2 to 3 (and is flipped at t = 0)
L1 goes from nodes 3 to 4
R2 goes from nodes 4 to 0

From simulation with the actual values I know this is an over damped circuit so the form of the equation should look like
V(t) = A1es1t + A2es2t
but I don't know if I can say it is a true RLC, or if I have to say it is a RC connected to an RL.

Any help to solve for A1, A2, s1, and s2 would be very, very helpful. Or telling me what is wrong with my theory would be great too. Thank you in advance!

Travis

p.s. - if you have the time, and are able to help, a walk through of how you obtained the equations would help me understand. Thanks!

p.s.s. - the actual values are as follows
C1 = 1.236 mF
R1 = 50.48 mΩ
L1 = 1.35 μH
R2 = 10.5 mΩ

2. Jun 27, 2012

### Carl Pugh

It's been many years and this is not my speciality, but
At t=0
C=1.236 mF
R=60.98
L=1.35μH
Voltage C=Vi
Current=0

Back when I was doing this, didn't use spice, just wrote the equations up in Basic. Results seemed to be correct.