An ac voltage v = vm sinωt is applied to a series LCR circuit. Obtain the expression for current in the circuit and the phase angle between current and voltage. What is the resonance frequency?

OR


An ac voltage v = vm sinωt is applied to a pure inductor L. Obtain an expression for the current in the circuit. Prove that the average power supplied to an inductor over one complete cycle is zero.



Current through resister, Vr=IᳵR


Current through inductor, VL=IL


Current through inductor, VL=



Now, impedance resistance is,


So, current, I=


The resonance frequency is the frequency in which Z=R, means XC=XL,


Or, L=


Or,


Or,


Or, This is the value of resonance frequency in LCR Circuit.


OR


(As, self induced voltage = applied voltage)





We know that, or


Or,


Now, average of is 0.


1