# Calculation of a voltage in the frequency domain

The current generator provides a constant current $I$ and the circuit is at règime conditions. At $t=0$, the switch T is being closed.

I have to calculate the voltage $v_c(t)$ by using the Laplace (unilateral) transform.

simulate this circuit – Schematic created using CircuitLab

After having calculated the initial condition (at $t=0^-$) $I_0$ and $V_0$, I can draw the circuit in the frequency domain, calculate $V_c(s)$ and antitrasform to get $v_c(t)$.

simulate this circuit

In the above circuit $R_1$ doesn't appear because it's shortcircuited, but why $I$ doesn't appear too? Could anybody explain-me just this, please?

The current source doesn't influence the circuit after the switch has closed because all the current it provides will flow through the switch itself, therefore it is not useful to the computation of $V_c$ in any way.
$I_x = I \cdot \dfrac {Z_{sw}} {Z_{sw} + Z_x}$
$I_x = 0$ if the switch is closed, i.e. if $Z_{sw} = 0$.