Calculate Voltage on Capacitor Over Time with RC Time Constant

[DIrtyPio]

Hi, I have a simple question: if I have a circuit with a capacitor, how do I calculate the voltage on the capacitor in function of time, I mean I know that tau(τ)=RC and there is the general formula X(t)=X(0)+[X(0)-X(∞)]^-t/τ. So here comes my question should I consider the capacitor as the load and calculate the Thevenin equivalent voltage at t=0 and t=∞ and use the X(t)=X(0)+[X(0)-X(∞)]^-t/τ formula ,where τ=R_ThC.

 

[Dale]

You can do it that way. A simple "rule of thumb" is that a capacitor is a short for high frequencies (t=0) and an open for DC (t=infinity).

 

[DIrtyPio]

Ok, I have some circuits and I don't know if I resolved the problems right so here are they:
and I have another question: files
1. The voltage of an ideal a.c. source has the expression:
u_g = 100 *2^0.5sin (2*10⁴ ∏*t +∏/3) V.
1.1. Find the value of the frequency and the value of the voltage at the moment t=0
1.2. Find the complex expression and the rms value of the current if the source supplies the impedance consisting in the resistance of 80 Ω connected in series with the inductance of 3/∏ mH (0.955 mH).

I don't really know what does it mean at the question 1.1. The frequency at the moment t=0. The voltage is 100 *2^0.5sin (∏/3).
The second question(1.2) I've solved like this:
U_RMS=100V ; R=80Ω ; L=3mH => X_L=j*2*10⁴∏*3/∏*10^-3=j*60Ω.
I_RMS=U_RMS/|Z|, where |Z|=(80²+60²)^1/2=100Ω => I_RMS=100/100=1A.
And the complex expression of the current is U_complex/R_complex=100^j∏/3/j60=100(cos∏/3+jsin∏/3)/j60=100(1/2+j3^1/2/2)/j60=50+j50*(3^1/2)/j60.

Is this correct?