^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.

^Power factor

Power factor is defined as, .

Its value lies between 0 & 1. To decrease the power loss in the transmission we have to increase the power factor, we can do this by making Z tend to R, for this we have to include a capacitor in the circuit.

^Average power consumed

Average power consumed in an ac circuit is:

P_average = E_v I_v cosΦ

E_v I_v → is called virtual power or apparent power.

^Reactance

Resistance offered by the L or C current in an ac circuit is called reactance. It is of two types

1. Inductive reactance X_L = ωL

2. Capacitive reactance,

Inductive reactance increases with the increase in frequency of ac. An inductor offers no resistance (X_L= 0) to dc, thus acts as short circuit for dc.

Capacitive reactance decreases with the increase in frequency of ac. A capacitor offers infinite resistance (X_C = ∞) to dc, thus doesn’t allow dc to pass through it & acts as open circuit for dc.

^Current in ac circuits

Let E = E₀ sin ωt is the sinusoidal source of emf applied to a circuit. Let Φ is the phase difference between current & the emf applied is, then the current flowing through the circuit can be represented by the general relation

I = I₀ sin (ωt + Φ), its virtual value of current is

Current flowing in a circuit depends upon following factors:

(a) input voltage signal

(b) frequency of the input voltage signal

(c) nature of circuit elements in the circuit

(d) combination of circuit elements in the circuit