How to connect LCR circuit in series combination

How to connect LCR circuit in series combination

Posted on August 20, 2016 by ezza

LCR circuit: Suppose a resistance R. an inductance L and a capacitance C are connected in series to a source of alternating emf

peak value of

Where emf of alternating current

Let I be the current in the series circuit at any instant. Then voltage will be differ due to R, L and C.

Potential across resistor:                                  R will be in same phase with

Potential across inductance coil                 Inductance L is ahead of current    by  

potential across capacitor                              Capacitance C lags behind the current   by 

Where    R    =   Resistance  I = current

                   Inductance reactance.

                 =    Capacitive reactance

As and are in opposite direction their resultant will be

The resultant of and must be equal to the applied emf

So using Pythagorean Theorem, we get

Where peak value of current

The effective resistance of series LCR circuit which opposes the flow of current is called Impedance. It is denoted by Z.

Impedance

Special cases:

(i) Inductive LCR circuit

When           or      

The emf is ahead of current by angle

        or       

The Instantaneous current

(ii) Capacitive LCR circuit

When          or    

The current is ahead of emf by angle

The Instantaneous current  

(iii) Resonance condition:        or  

Clearly the circuit is purely resistive

The current and voltage are in same phase and the current is maximum. This is Resonance condition