Double RC circuit with a leading phase voltage source, phase shift, "EXO N°10 Video 2, 2 "

a second-order filter circuit, consisting of two capacitors and two resistors, is supplied with a sinusoidal voltage source whose initial phase is not zero. Determine the currents flowing through each element of the circuit and the voltages manifested at their terminals, as well as their phase shifts.
Method:
1) Start by transforming the reactive “C” capacitors into their frequency-domain equivalents, using complex numbers or moduli and phases. Similarly, we transform the voltage source into a module and phase.
2) Once all circuit parameters have been converted to modulus and phase, or to complex numbers, the circuit is analyzed in the frequency domain.
3) Frequency analysis results in currents and voltages in modulus and phase form in the frequency domain.
4) The modulus and phase of each voltage and current can be used to
voltages and currents on an orthonormal reference frame.
5) These plots can be used to visualize the phase shifts between the circuit's currents and voltages. However, the phase shifts can also be seen by observing the phase angles, one in relation to the other.
6) Finally, the modulus and phase of each frequency-domain voltage and current can be transformed back into their equivalent time-domain expressions, depending on the variable “t”.
In fact, all you have to do is write the cosine function for each voltage and current, since the phasors, i.e. the moduli and phases, are derived from the cosines:
V(t)=COS(W.t+phaseV°) and I(t)=COS(W.t+phaseI°) , where W is known and in [Rad/s], and phaseV° represents the phase angle of a voltage, and phaseI° is the phase angle of a current.
Note: A capacitor C or an inductor L is a reactive element. If a circuit has only one reactive element, it is said to be of first order; if it has “n” reactive elements, it is said to be of Nth order. In this case, we have two capacitors, so the circuit is second-order.
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