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
• determine the and the frequency at which this occurs
• determine the overall in series
• define bandwidth
• calculate Q-factor circuit
• determine the current deviates from the resonant frequency
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 phenomenonof 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) In electrical work there are two types of resonance –
one associated with series circuits (which was introduced in Chapter 17), when the input impedance is a minimum (which is discussed further in this chapter), and the other associated with simple parallel networks, when the input impedance is a maximum (which was discussed in Chapter 18 and is further discussed in Chapter 32).
