Resonance In Series LCR Circuit - Practice Questions & MCQ

Resonance in Series LCR circuit-

As we have discusssed that when- 

                                               ,

then tanφ is zero i.e. phase angle (φ) is zero and voltage and current are in phase. We have called it electric resonance. So, if , then the equation of impedence become - 

                                                                   

So, we get minimum value of Z. 

In this case impedance is purely resistive and minimum and currents has its maximum value. Now as - 

 

                                                                                

                                                                So,

                                                                                   

As,  .  Where  is the frequency of applied voltage.

                                   

                                                                So,

                                                                              

This frequency is called resonant frequency of the circuit. 

Peak current in this case is given by - 

                                                                           

We will now discuss about the resonance curve and its nature. We will show the variation in circuit current (peak current i₀) with change in frequency of the applied voltage - 

                                   

This figure/graph shows the variation of current with the frequency. 

Conclusions from the graph - 

1. If R has small value, the resonance is sharp which means that if applied frequency is lesser to resonant frequency f₀,the current is high otherwise

2. If R is large, the curve is broad sided which means that those is limited change in current for resonance and non -resonance conditions

                  

Note -                                

The natural or resonant frequency is Independent from resistance of the circuit.