# Calculation of a current at règime

I have to calculate $i(t)$ at règime, by knowing that $v_s(t)=2\cos(\omega t + \pi/2)$, $R=1\Omega$, and that, at the generator frequency, $X_c=-1\Omega$ and $X_L=1\Omega$. simulate this circuit – Schematic created using CircuitLab

I know how to solve this by using the phasor domain. That is: using the current divider formula (after I substituted the series $v_s\ -\ R$) with the Norton equivalent (current generator $v(s)/R$ in parallel with $R$).

But something just came across in my mind: at règime, doesn't the inductor and the capacitor behave, respectively, as a short circuit and an open circuit? By reasoning that way $$i(t)=\frac{v(s)}{2R}=\frac{\cos(\omega t + \pi/2)}{R}$$

But how can I proceed? Is it correct to reason that way?

• What does "at regime" mean? Jun 15, 2015 at 20:52
• After a sufficient time such that the temporary effects have gone away. Jun 15, 2015 at 20:54
• I would call it "steady state" Jun 15, 2015 at 20:54
• The usual word for that in English is "in steady state". Jun 15, 2015 at 20:54
• Anyway. The inductor and capacitor are "short" and "open circuit" in steady state, only if the steady state is for DC. In your case it's AC, so the components response is not that simple (phasors, as said). Jun 15, 2015 at 20:56