# Differential equation that describes the voltage with respect to time

1. Sep 16, 2014

### DustyGeneral

In class we discussed RLC circuits in series. My homework problem, however, has me analyzing an RLC circuit in series.

a) Write the differential equation that describes the voltage with respect to time.
b) Find the natural frequency of oscillation and the damping constant of the circuit.

I know that because they are connected in parallel they all have the same voltage across them, and because we are studying damped harmonic oscillators that the equation should resemble that of a damped harmonic oscillation.

Do the same aspects of a series circuit apply? For example:

VsubC = q/C
VsubL = LI'
VsubR = IR

or are they completely different for a parallel? I just need a push to get on the right track.

2. Sep 16, 2014

### nrqed

I guess you meant "parallel" in that last sentence.
These equations still apply, they are completely general. The difference with the series case is of course that now the voltage across all elements is the same at any value of t.