Circuit Analysis Using Laplace Transform Problem

laplace transform circuit analysis

This question is more of a circuit question than that of a math problem it's a simple problem.

I know how to set up the equaiton using the laplace transforms, but I do not know how to set up the initial conidition for il(o-) and vc(o-), and so I'm having problems setting up the equation.

I posted the problem if anyone can help I would really appreciate it.

circuit analysis using laplace

There was an Ebook about 'Network Analysis' posted some time ago. You should be able to find answers to your question there.

circuit analysis using laplace transform

check this book also
engineering circuit analysisby
william h . hart
jack e. kemmerly
steven m. durbin

laplace rl circuit

When the switch is closed the inductor of 1 H and the capacitor are out of the circuit once the switch short circuit them.

When the switch opens, they sundenlly become part of the circuit.

In t(0-) the capacitor is completely discharged since the switch was closed for a long time, so the voltage across its terminals is 0 Volts, so in t(0+) the current through it should be maximum since it has no charge. On the other hand, the inductor offers a high oposition to rapid current variation, so at t(0+) it behaves like a open circuit and has all the voltage across its terminals, as consequence, the initial current acroos it is zero.

With this analisys you are able to set the initial conditions:

Vc(0+) = 0 and IL(0+)=0.

Regards
Claudio

laplace transform problems

Hi!

I'm of the opinion that a howler has been made in the previous post! If the switch has been closed a long period of time since the 9V source was applied then the 1H inductor can be assumed, ***immediately before opening the switch***, to be a short circuit since an inductor only resists changes of current, and in a DC RL circuit, the only effective impedance is the resistor, then:-

i(0-) can only be 9/6 = 1.5A giving I(s) = 1.5/s

The switch is assumed to have been closed a long time so if all initial charges on the capacitor have assumed to have decayed then vc(0-) = 0.

Chris Williams