RL circuit with independent sinusoidal voltage source, phase shift, "EXO N°6 Vidéo 2, 2 "

With a resistor R and an inductance L connected in series and supplied by a sinusoidal voltage source, determine the expression for the current flowing through the inductance and the variation in current intensity as a function of time.
To do this, we transform the inductance L and the voltage source V(t) into complex numbers expressed as modulus and phase (modulus/phase°), called phasors, and from the moduli and phases of the voltage and reactance XL, we deduce the modulus and phase of the current via Ohms' law. Moduli and phases of voltages and currents make it easy to visualize phase shifts.
Note: when we analyze a circuit via moduli and phases, or simply in complex numbers, this means that the circuit is analyzed in the frequency domain, and the results found belong to the frequency domain since they do not contain the variable ' t ' .
The modulus and phase of each voltage and current found in the frequency domain can be transformed back into their equivalent expressions in the time domain, depending on the variable t .
In fact, all we need 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.
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