00:01
Hello in the question it is given consider one lcr circuit in which l, c and r are connected in series so inductor capacitor and resistor that is l, c and r are connected in series and together they are connected to a variable source of for volt that is v is equal to 230 volt since it is the ac circuit there is no frequency frequency is wave varying and l value is equal to 5 henry capacitance is equal to 80 microfarrid that is nothing but 80 into 10 per minus 6 fared and resistance value is given that is 40 own and we need to calculate the frequency which drive the circuit resonant that is resonant angular frequency omega not that we need to calculate also obtain the impedance of the circuit and the amplitude of current at the resonant frequency, that is impedance value, also the amplitude of current, that is maximum value of current, that is im.
01:18
So these are the values that we need to find out.
01:22
So first we will calculate a resonant angular frequency, that is, omega -0 is given by 1 divided by root l into c, that is equal to 1 -divided by root l, that is 5 into 8 .000.
01:41
Into 10 to 0 .10 .5 .6.
01:44
That is nothing but 1 divided by root 40 into 10 to minus 6.
01:49
So calculating omega -0 is equal to 50 radian per second.
01:55
So this is the value of resonant angular frequency of the circuit.
01:59
Next we will calculate the impedance z value.
02:03
That is impedance z is given by square root r square.
02:14
Plus xl minus that is xl square sorry xl minus x c whole square where x l is the inductive reactants that is given by the equation omega l and x c is the capacitive reactants that is given by 1 divided by omega c here omega not we need consider now substituting in this equation that is r square plus omega not l minus 1 divided by omega not c to the power 2.
02:51
And so at resonance, xl must be equal to xc.
03:00
That is, xl minus xc value must be equal to 0...