^LCR series or acceptor circuit

If the generator oscillates at a frequency equal to natural frequency of LC oscillator then current in the circuit becomes maximum & the stage is called resonance. Following points are of interest at resonance.

1. X_L= X_C, Z = min. = R

2.

3. Φ = 0

4. Quality factor or Q factor or voltage multiplication factor is defined as the ratio of voltage across inductor (or capacitor) V_L (or V_C) to ratio of voltage across a resistor at resonance. i.e.

5. Also

Here ω₁ & ω₂ are called half power side band frequency.

6. Value of Q describes the sharpness of I – ω curve at resonance.

If band width is low, the quality factor will be high & the I – ω graph will be thin & sharp & vice – versa as shown in the following plots. Higher the value of Q-factor, the narrower & sharper is the I – ω curve at resonance.

The larger the value of Q – factor, the smaller is the value of 2 Δω or the bandwidth and sharper is the resonance.