ABSTRACT
At the end of this chapter you should be able to: • state the conditions for resonance in an a.c. series circuit
• calculate the resonant frequency in an a.c. series circuit,
fr = 12π√(LC) • define Q-factor as X
R and as
VL V
or VC V
• determine the maximum value of VC and VCOIL and the frequency at which this occurs
• determine the overall Q-factor for two components in series
• define bandwidth and selectivity • calculate Q-factor and bandwidth in an a.c. series circuit
• determine the current and impendance when the frequency deviates from the resonant frequency
28.1 Introduction
When the voltage V applied to an electrical network containing resistance, inductance and capacitance is in phase with the resulting current I , the circuit is said to be resonant. The phenomenon of resonance is of great value in all branches of radio, television and communications engineering, since it enables small portions of the communications frequency spectrum to be selected for amplification independently of the remainder. At resonance, the equivalent network impedance Z is
purely resistive since the supply voltage and current are in phase. The power factor of a resonant network is unity (i.e. power factor= cos φ = cos 0= 1).
