Question

Q factor of series resonant circuit is?
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Answer 1

Answer:

Bandwidth of a Series RLC Resonance Circuit

bandwidth of a series rlc resonance circuit

Then the relationship between resonance, bandwidth, selectivity and quality factor for a series resonance circuit being defined as:

1). Resonant Frequency, (ƒr)

resonant frequency

2). Current, (I)

series circuit current

3). Lower cut-off frequency, (ƒL)

lower cut-off frequency

4). Upper cut-off frequency, (ƒH)

upper cut-off frequency

5). Bandwidth, (BW)

series circuit bandwidth

6). Quality Factor, (Q)

quality factor

Series Resonance Example No1

A series resonance network consisting of a resistor of 30Ω, a capacitor of 2uF and an inductor of 20mH is connected across a sinusoidal supply voltage which has a constant output of 9 volts at all frequencies. Calculate, the resonant frequency, the current at resonance, the voltage across the inductor and capacitor at resonance, the quality factor and the bandwidth of the circuit. Also sketch the corresponding current waveform for all frequencies.

example no1 series circuit

1. Resonant Frequency, ƒr

circuits resonant frequency

2. Circuit Current at Resonance, Im

circuit current

3. Inductive Reactance at Resonance, XL

inductive reactance

4. Voltages across the inductor and the capacitor, VL, VC

Inductor and Capacitor Voltages

Note: the supply voltage may be only 9 volts, but at resonance, the reactive voltages across the capacitor, VC and the inductor, VL are 30 volts peak!

5. Quality factor, Q

circuits quality factor

6. Bandwidth, BW

bandwidth

7. The upper and lower -3dB frequency points, ƒH and ƒL

cut-off frequency equation

8. Current Waveform

current waveform