 I, Mrs. Veena Sunil Patki, Assistant Professor, Department of Electronics Engineering, Walshan Institute of Technology, Solapur, welcome you for this session. At the end of this session, students can analyze RC series circuit through AC. So, register and capacitor are connected in series, R is measured in terms of ohms, AC is measured in terms of Farad, V equal to Vm sin omega t, AC voltage is connected across series register and capacitor circuit. So, Vr is given by I into R, Vc is given as I into Xc, where Xc is the capacitive reactance in ohms equal, Xc equal to 1 upon 2 pi fc, where f is the frequency of the supply. So, total voltage V is the vector sum of Vr and Vc, for resistive circuit Vr and I both are in phase, for capacitive circuit, current is leading to voltage by 90 degree, so step by step we will discuss about the phasor diagram. So, current I is taken as a reference, because current is same for both register and capacitor. Vr is in phase with current I, Vc lags current I or we can also say that current leads Vc by 90 degree for this capacitive circuit. And as current leads voltage by angle of 90 degree in pure capacitive circuit, the vector sum of 2 voltage drops Vr and Vc is equal to applied voltage. So, to draw that total voltage, first we are going to draw the parallelogram for this and then this is the total voltage V and this is the theta angle between voltage and current. You can see here the current leads voltage by theta degree. So, from this phasor diagram we can draw the voltage triangle, this is the voltage triangle and from this voltage triangle we can write down this V equal to Vr square plus Vc square. So, after putting that Vr equal to I into R and Vc equal to I into Xc, we will get the equation like this and by taking that current as a common, we will get the equation V equal to I under root R square plus Xc square and Z equal to under root R square plus Xc square. So, here we can write down that V equal to I into Z, where Z is the impedance measured in ohms. From this voltage triangle, we can draw the impedance triangle like this, simply eliminate the current from that I R, I Xc and I Z, we will get the impedance triangle like this and we can write down the impedance as under root R square plus Xc square. In rectangular form Z equal to R minus J into Xc. In polar form Z equal to magnitude of Z and angle of minus theta. So, phase angle, so from this voltage triangle and impedance triangle in RC circuit current leads voltage by theta angle that is called as the phase angle and we can write down tan theta as Vc by Vr equal to I Xc into divided by I R or tan theta equal to Xc by R and theta equal to tan inverse of Xc by R that is the phase angle for this RC series circuit. We can also write down the voltage equation and current equation V equal to Vm sin omega t and I equal to Im sin omega t plus theta. Now, pause the video and think what is the relation between current and voltage for RC series circuit. So, what is the answer? If the voltage equation is V equal to Vm sin omega t and I equal to Im sin omega t plus theta then what is the relation? Current leads voltage by theta degree that is the answer for this question. So, here from this phasor diagram you can see the current leads voltage by theta degree. Now, we can draw the power triangle from this voltage triangle. So, here the active power P is given by I into Vr or we can also write down that as Vi cos theta and active power is measured in terms of watts. So, reactive power is given by Q equal to I into Vc or we can also write down that as a Q equal to Vi sin theta. Reactive power is measured in terms of Var that is nothing but volt ampere reactive. So, apparent power as is given by V into I or I into V and measured in terms of volt ampere that is nothing but Va. So, the power factor for this RC series circuit we can write down that from voltage triangle from impedance triangle and from power triangle. So, cos theta equal to Vr by V equal to r by z equal to P by s and power factor here is the leading power factor because the current leads voltage by theta degree for RC series circuit. So, power in RC series circuit we can calculate as now we can calculate the power in RC series circuit. Alternating voltage applied to RC series circuit is given by V equal to Vm sin omega t. Current equation is given by I equal to Im sin omega t plus theta because current is leading to voltage by theta degree and the instantaneous power is given by P equal to V into I. By using this above equations we can write down the power equation as Vm sin omega t into Im sin omega t plus theta. So, P equal to Vm Im by 2 cos theta minus cos 2 omega t plus theta by using trigonometric formula. So, here we can also write down that equation as Vm by root 2 Im by root 2 cos theta minus cos 2 omega t plus theta only by splitting that 2 as a root 2 into root 2. Now split that 2 terms we will get the equation P equal to Vm by root 2 Im by root 2 cos theta minus Vm by root 2 Im by root 2 cos 2 omega t plus theta. Now we can calculate the average power by using this equation. So, average of this first term minus average of this second term. So, average of that second term is 0 because average of cos theta is nothing but 0 and here we will get the equation as P equal to average of Vm by root 2 Im by root 2 cos theta minus 0. So, Vm by root 2 is Vrms and Im by root 2 is Irms. So, we can write down the power equation P equal to Vrms Irms cos theta. So, generally we can write down the power equation as P equal to Vi cos theta in terms of watts and the cos theta is nothing but the power factor of the circuit that is given by Vr by Vr by Z and P by S and the power factor is always leading for RC series circuit because the current leads voltage by theta degree. We can draw the voltage current and power cycle like this. You can see here the cycles, power cycles, voltage cycle and current cycle. So, current leads voltage by theta degree that power cycle indicates that positive part for that is greater means circuit contains register more as compared to capacitance. So, you can refer the book Electrical Technology by B. L. Therese. Thank you.