Points to Remember in Series Resonance Circuits

Points to Remember in Series Resonance Circuits

1. When the series A.C. circuit is at resonance

(a) E and I are in phase, (b) Power factor is unity.

(c) The circuit acts as purely resistive

(d) The impedance is minimum and hence current maximum.

 (e) The net reactance is equal to zero. i.e., (XL – XC = 0).

(f) In the rectangular form, reactive part of Z = 0 and also reactive part of Y = 0.

(g) Maximum current = E / R

 (h) Power absorbed is maximum and is given by:

E × I × cos ϕ = E × E/R × 1 = E2/R

2. For RLC series circuit, when the frequency is lesser than fo, Xc > X. So, net reactance is capacitive. The impedance is capacitive. Hence, power factor is leading i.e., current leads the applied voltage.

3. For a frequency more than fo, XL is more than XC. The impedance, is inductive. So, the power factor is lagging in nature.

4. Quality factor is equal to 

5. At resonance all the applied voltage is across resistance i.e., ER = E.

6. The current at resonance is limited only by resistance.

7. There is voltage magnification in series resonance.

8.Voltage magnification EL or EC / E at resonance Q. At half power frequencies, the power factor is 0.707. It is lagging in nature at f2 and leading in nature at f1.

9. Bandwidth of series resonance circuit is given by the band of frequencies which lie between the 2 points on either side of the resonant frequency = f2 - f1.

10. Half power points are the points on current versus frequency curve corresponding to half power frequencies. At half power points, the power dissipated in a circuit is equal to half the power at resonance.

11. f1, fo and f2 are in geometric progression i.e., f1 f2 = fo2.

12. Selectivity of a resonant circuit is its ability to discriminate between signals of desired and undesired frequencies. It is defined as the ratio of resonance frequency and bandwidth.

13. When the frequency is varied, Ec is maximum at a frequency less than resonance frequency.

14. When the frequency is varied, EL is maximum when the frequency is greater than resonance frequency.