What is RESONANCE in series RLC circuit????

• RESONANCE:-

➝ " It is the phenomenon at which the effect of Inductive reactance (XL) and Capacitive reactance (XC) are compensated to each other in RLC circuit is called as a RESONANCE".

➝At the time of resonance circuit is behaves as a pure resistive circuits and at the time of resonance power factor of the circuit is UNITY.

❋RESONANCE IN SERIES RLC CIRCUIT:-

Fig(a) SERIES RLC CIRCUIT

⇨The Impedance Z of series RLC circuit is given as;

                 Z = R + jwL + j 1/WC

            ∴.  Z = R + wL - j/wc ................(1)

Magnitude

 |Z| = √R^2 + j( wL - 1/WC)^2 ...........(2)

➝ Current in RLC resonance circuit is;

                  I = V/Z amp. ..........(3)

          I = V/ √R^2 + j(wL - 1/WC)^2 ㄥ tan-1 (wL - 1/WC)/R   ...................(4)

• AT THE TIME OF RESONANCE XL = XC ;

                 XL = XC

              W0L = 1/ W0C 

               W0^2 = 1/ LC

          ∴ W0  = 1/ √LC rad/ Sec ...........(5)

• Frequency at the time of resonance ;

                     

                   W0 = 1/ √LC rad/ sec ....... ..(6)

                    

                   F0 = 1/ 2π√LC Hertz (Hz) .......(7)

❋ PROPERTY OF SERIES RLC RESONANCE CIRCUIT:-

⇾At the time of resonance the applied voltage is in phase with resultant current, it means the power factor is unity (COSΦ = 0).

⇾At the time of resonance the effects of XL &XC are compensated to each other, therefore the behaviour of the network is purely RESISTIVE.

⇾At the time of resonance the Current I = V/R amp. And it's value is maximum because total impedance of the circuit at the time of resonance is only "R" so I is maximum according to ohms law.

⇾At the time of resonance the Impedance Z is minimum.

           .................... Thank you 🙂................