# RLC circuit, finding relations and forming a differential equation

1. Dec 5, 2012

### Cave Canem

Hello. I'm having a hard time solving this homework question, even though I know I shouldn't... but well.

Here's the problem :

-The K switch is closed for a long time, so as to be in a steady state.
What's the electric charge of the capacitor ? Infer vs tension from this.
Which current is crossing the inductor ?

My guess : Charge is 0 because it is totally decharged. The tension of the capacitor is equal to vs so vs=0. The current from the generator is crossing the inductor.

-At t=0 we open the switch. Find five relations between i, ic, ir, q, and vs, and form a differential equation with vs

So we have
i=ic+iR

I am not sure about tensions... let uc=capacitor tension, ur= resitance r tension, uR = resitance R tension

is E=ur+uL=uc=uR ?

if yes then we have E=vs+Ldi/dt and I could find a differential equation with i=ic+ir and replacing ic and ir by ic=C*uc/t and iR=uR/R but it would be useless since E=uc=vs...

to make it short, I don't get how I can find these relations, please help me.. thanks