# Circuit Analysis with Laplace Transforms

1. Nov 2, 2016

### gmm

1. The problem statement, all variables and given/known data

2. Relevant equations
V=IR
All of them actually

3. The attempt at a solution
So I Started off by transforming the voltage source into the 's' domain
vs(s) = (4/s) -(4/s)*e-.5t

I know the initial conditions are zero, in other words at t=0, the voltage and currents at the capacitors are all 0. which means that that my capacitor 1 can be expressed as an impedance: 106/s. and capacitor 2 as : 3*105/s. All the resistors stay the same.
So now the circuit is transformed into the 's' domain which basically means its comprised of one voltage source and 5 impedences?
This is kind of where I'm stuck... I know that for a Capacitor in the 's' domain the voltage is Ic/sC + vc(0-)/s.. in this case Initial conditions are zero so for both capacitors Vc = Ic/sC ... I now need to find the current I at each capacitor right?
If so I'm not sure how to go about this, all of the examples in my book only show steps for circuits that have components either all in series or all in parallel. Node Voltage Analysis? Current Mesh Analysis? Whats my next step??

2. Nov 2, 2016

### Staff: Mentor

Node voltage analysis (nodal analysis) looks like a good choice: There's only one essential node.

The Laplace impedance of a capacitor is $\frac{1}{sC}$.

3. Nov 2, 2016

### Hesch

Calculate the transfer functions v1(s)/vs(s) and v2(s)/vs(s).

( Calculate the current, I(s), through the 4 rightmost components. Then v(s) = Z(s) * I(s) for both RC pairs. )

Knowing e.g. v2(s)/vs(s) → v2(s) = v2(s)/vs(s) * vs(s).

Then inverse Laplace transform.

4. Nov 3, 2016

### rude man

I suggest labeling your components C1, C2, R1 etc rather than working with numbers up front. Then you can also use dimensional analysis for checking the math. Otherwise you're on the right track.