# Laplace tranforms, transient current series CR circuit

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1. May 7, 2017

### DanRow93

1. The problem statement, all variables and given/known data
A step voltage of 120v is applied to a series CR circuit. R = 20KΩ, C = 4µF

1. Deduce, using Kirchoff's voltage law and Laplace Transforms, an expression for the transient circuit current.

2. Using the equation obtained in 1. deduce the equations for the transient voltages across the resistor and capacitor.

2. Relevant equations
V = vc + vr
vr = iR
i = C dvc/dt
vr = CR dvc/dt
V = vc + CR dvc/dt

3. The attempt at a solution
I am first trying to find the transient circuit current, so I will use the equation i = C dvc/dt

Using Laplace Transforms gives i/s = C (sV(s) - vc(0))

vc(0) = 0

So i/s = C (sV(s))

i/s = (4x10^(-6))(sV(s))

i/(4x10^(-6)s) = sV(s)

I'm stuck here, I can't seem to find a Laplace Transform to put the equation into the (t) domain?

Or should I have started with the equation V = vc + CR dvc/dt

2. May 7, 2017

### Staff: Mentor

You can bypass the differential equation interpretation if you simply replace each circuit component with its Laplace Domain counterpart, then write the usual circuit equations using them. The voltage source is a step function, so that's trivial, and use the "Laplace Impedances" for the other components:

$V \rightarrow \frac{V}{s}$
$R \rightarrow R$
$L \rightarrow L s$
$C \rightarrow \frac{1}{sC}$

3. May 19, 2017

### rude man

This equation is wrong.