 Myself, Mrs. Veena Sunilpatki, Assistant Professor, Department of Electronics Engineering, Valkan Institute of Technology, Solapur. Welcome you for this session. At the end of this session, students can solve numerical on RLC series circuit through AC. So, let us see first numerical. So, here the circuit is given for the circuit shown in the figure, right? Expression for current, phase difference, frequency and calculate the RMS value of current. So, from this diagram, we can write down the given data as, so here the resistance is given R equal to 200 ohm, inductance is given 638 millihenry, so 638 into 10 raise to minus 3 henry, so convert that millihenry to standard unit, then voltage is 200 sine 80 pi t. So, from this equation, we can write down the maximum voltage as 200 volt omega equal to 2 pi f equal to 80 pi and from this we can calculate the frequency as 40 hertz. So, we can calculate the RMS voltage from this maximum voltage, so RMS voltage equal to maximum voltage divided by root 2 equal to 200 by root 2 equal to 141.42 volts. So, excel equal to, first we are going to calculate the excel because L is given here, so excel equal to 2 pi f L equal to omega L, directly omega is given otherwise we can use the 2 pi f L formula also. So, excel equal to omega L equal to 80 pi into 638 into 10 raise to minus 3, so excel equal to 160.34 ohm. So, we can write down the impedance as z equal to R plus j excel equal to 200 plus j 160.34 ohm. So, we can calculate the impedance by using the formula z equal to under root R square plus excel square equal to under root 200 square plus 160.34 square equal to 256.38 ohm and theta is given by tan inverse of excel by R equal to 38.72 degrees, so z we can write down in polar form as 256.38 angle of 38.72 ohm. So, we can calculate the IRMS equal to VRMS divided by z equal to, so after calculating 141.42 divided by 256.34 we will get IRMS at 0.55 and here we can calculate the angle as 0 minus 38.72 that is minus 38.72. So, the current lags voltage by 38.72 degrees and the phase angle theta is given by 38.72, so current equation we can write down as I equal to IM sin omega t minus theta, so maximum current is IM equal to under root 2 into IRMS equal to root 2 into 0.55 equal to 0.78 ampere and current equation is given as 0.78 sin of 80 pi t minus 38.72 degrees, so we can summarize the answer as expression for the current is I equal to 0.78 sin of 80 pi t minus 38.72 degrees, phase difference theta equal to 38.72 degrees, frequency is given as 40 hertz and RMS value of the current is I RMS equal to 0.55 ampere. Now, pause the video and think about this question. Under the condition of resonance in RLC series circuit, the power factor of the circuit is A 0.5 lagging, B 0.5 leading, C unity and D 0. So, what is the answer here? Answer is C that is unity because for resonance, the unity power factor is the main condition and excel equal to xc or we can also say that the voltage across inductive reactance and voltage across capacitive reactance is also same. So, under the condition of resonance, the power factor is unity. Let us solve the second numerical. A series RLC circuit consists of R equal to 10 ohm, L equal to 0.318 Henry, C equal to 63.6 microfarad and EMF source V equal to 100 sin of 314 t. Calculate one expression for the current, second phase angle, third power factor, fourth active power and fifth draw the phasor diagram. So, let us see the given data that is R equal to 10 ohm, L equal to 0.318 Henry, C equal to 63.6 microfarad equal to 63.6 into 10 raise to minus 6 farad and V is 100 sin 314 t. So, from this voltage equation, we can write down the maximum voltage equal to 100 volt and omega equal to 314. So, the RMS voltage we can calculate from the maximum voltage as V RMS equal to Vm by root 2 equal to 100 by root 2 equal to 70.71 volts. And from inductance, we can calculate the inductive reactance equal to omega L equal to 314 into 0.318 equal to 99.85 ohm. And we can also calculate from capacitance value that is Xc, capacitive reactance equal to 1 upon 2 pi fc equal to 50.07 ohm and Z equal to under root R square plus Xl minus Xc bracket square. So, after putting the values of Xl and Xc and R here, we will get the value of Z as 50.77 ohm and theta equal to tan inverse of Xl minus Xc by R. After putting the values of Xl and Xc and R here, theta equal to 78.61 degrees. So, here we can calculate current as V by Z equal to 70.71 angle of 0 divided by 50.77 angle of 78.61. So, current equal to 1.39 after calculating 70.71 divided by 50.77 we will get I as 1.39 ampere and angle is here 0 minus 78.61. So, current is given by 1.39 angle of minus 78.61. The maximum current we can calculate that is root 2 into IRMS equal to root 2 into 1.39 equal to 1.96 ampere and we can write down the current equation as I equal to 1.96 sin of 314 T minus 78.61 degrees. So, phase angle theta equal to 78.61 lagging because the circuit is inductive in nature and power factor is calculated as cos theta equal to cos of 78.61 equal to 0.97 lagging and we can calculate the active power P equal to Vi cos theta. So, after putting the values of Vi and cos theta here active power is equal to 19.39 watts. First we are going to calculate the VR as equal to IR equal to 1.39 into 10 equal to 13.9 volt, VL equal to I into XL equal to 139.065 volt and VC is given as I into XE that is 69.73 volt and the resultant voltage VL minus VC is given as 69.326. So, here the total voltage V is 70.71 volt and theta equal to 78.64. For phasor diagram first we are going to draw the current vector then VR is in phase with current VC is lagging to the current and VL is leading to the current and here we will get the resultant voltage VL minus VC upside. So, to calculate the resultant voltage here we are going to add VL minus VC to VR and here we will get the total voltage V equal to 70.71 and the theta is given as 78.64 degrees. So, you can see here the current is lagging to the voltage by 78.64 degrees. You can refer the book Electrical Technology by B.L. Thareja. Thank you.