Lecture A

Lecture session

Place  SRTC 228 

LECTURE A    Complex Impedance                                                                                                  Tuesday      01-09-2024
                               Complements:  Complex Numbers 
                                                                  Solution of the forced harmonic mechanical oscillator usingphasors 
                                                                  Representation of harmonic waves using phasors

PURPOSE

A background on the concept of complex impedance of capacitors and inductors is provided to obtain a better understanding of their frequency-dependence response in an alternating current (AC) circuit. These concepts are applied to the case where a resistor, a capacitor and an inductor are connected in series. The analysis is undertaken using complex variable.

THEORETICAL CONSIDERATIONS

I. Impedance     

    IA.  The RLC Circuit in series

    IB   Relationship between the voltage and current across each element

      Resistance

      Capacitor complex impedance

      Inductor complex impedance

II.   Kirchhoff law for the RLC circuit

III.  How to calculate and measure current amplitude Io(w) and  phase lag j (w) ?

           Complex impedance of the RLC-series circuit

      Calculation of  Io  and  j   

    IV.  Resonance

                 Resonance condition

Relative orientation of the phasors input voltage vA and current response i at different values of w

                 Example: Analysis at resonance and  out of resonance conditions