Question

How do I calculate the currents of the following circuit with an applied AC voltage of :
ε(t) = ε0 exp(iωt)

Answer 1

hint:
we can start, writing the Ohm's law for the circuit:
\[\Large V = {Z_{TOT}}{I_1}\]
where the toatl impedance \(Z_{TOT}\) checks these conditions:
\[ \Large \begin{gathered}
{Z_{TOT}} = {Z_1} + Z' = {R_1} + Z'

\end{gathered} \]
\[\Large \frac{1}{{Z'}} = \frac{1}{{{R_2}}} + \frac{1}{{i\omega L}} + i\omega C\]

Answer 2

with:
\[\Large V\left( t \right) = \mathcal {E}\left( t \right)\]

Answer 3

if we are searching for transient state, then the equations are different, of course

Answer 4

There are a number of ways to tackle this problem.
Which method do you use to analyse ac circuits?