 I am SSVS Patki, Assistant Professor, Department of Electronics Engineering, Valkan Institute of Technology, Solapur. Welcome you for this session. At the end of this session, students can simplify the purely resistive circuit for AC supply. So purely resistive circuit means only resistance is connected to AC supply. So here you can see here one resistance is connected across AC supply. This AC supply is given by V equal to Vm sin omega t, where V is the instantaneous voltage, Vm is the maximum voltage and omega is the angular frequency and t is the time. This instantaneous voltage changes with respect to time. So if we connect this AC voltage to this purely resistance, we have to discuss the relation between this voltage and current flowing through this resistance. So resistance is the property which oppose the flow of electrons. So due to that, resistive voltage drops across this resistance that is Vr. This Vr is given by I into R according to Ohm's law, where I is the current flowing through this resistance and R is the resistance in Ohm's. So this Vr is same as the applied voltage that is Vm sin omega t. So we can write down this equation as Vr equal to Ir equal to Vm sin omega t. So we can write down this equation as I equal to Vm by R sin omega t. So in this equation Vm by R is the current, maximum current. So here we can write down this maximum current that is Im equal to Vm by R. So by replacing this Vm by R by Im in this equation, we can write down this current equation as I equal to Im sin omega t. So if we compare this voltage equation and this current equation, here you can see the angle that is omega t is same. That means voltage and current both are in phase. So phase difference for this voltage and current is 0. So we can draw the cycles. So here time you can consider here voltage or current on y axis. So this is the voltage cycle. Voltage and current both are in phase means both voltage and current starts its cycle at the same time and reaches its maximum value at the same time. So we can draw the current cycle here like this. So voltage and current both are in phase. So we can draw the phasor diagram. So this is the phasor for voltage and this is the phasor for current. So voltage and current both are in phase. So on same phasor we can draw voltage and current here. Theta is 0. So power factor for this circuit that is cos theta is given by cos 0 equal to 1. That is called as unity power factor. So here we can say for purely resistive circuit the phase difference for voltage and current is 0 and power factor is unity for this circuit. Now we can calculate the instantaneous power for this circuit. So instantaneous power is given by P equal to V into I. Voltage is given by Vm sin omega t. Current is given by Im sin omega t. So the equation becomes Vm Im sin square omega t. So we can use the formula for sin square omega t Vm Im 1 minus cos 2 omega t by 2. So if we use this formula we will get the instantaneous power as Vm Im by 2 minus Vm Im by 2 cos 2 omega t. Now you can see the power equation where the two terms are there one is the constant term and another is the variable term and if we calculate the average power for this average of cos 2 omega t is 0. So we will get the equation as Vm Im by 2 and we can write down this equation as Vm by root 2 into Im by root 2 where Vm by root 2 is Vrms and Im by root 2 is Irms. So we can write down this power equation as Vrms into Irms. So we will get the average power as Vrms into Irms. Now you can see the equation power equation here cos 2 omega t is there and angle is 2 omega t. In this voltage equation angle is omega t so power cycle has the double frequency than the voltage cycle. Now we can draw the cycles for this power and we can prove that graphically also here you can see here the power has the double frequency by mathematically you can see here. So we can draw the power cycle. So see here, so this is the time you can consider here voltage current or power also. So here the voltage cycle current is in phase with this so here we will get the current cycle then power is nothing but the product of voltage and current. So for this first half cycle voltage and current both are positive. So product is here positive so we will get the here power cycle. For this next half cycle voltage and current both are negative but the product of this is positive. So we will get the cycle like this so this is the power cycle. So both power cycles are positive here. So you can see here one voltage cycle has two power cycles. So you can see graphically also the power cycle has the double frequency than the voltage cycle and both positive cycle indicates that in purely resistive circuit continuous power consumption will be there. Now pause the video and think what is the phase difference between voltage and current for purely resistive circuit? Yes, what is the answer? For purely resistive circuit phase difference is 0. You can refer the book Fundamentals of Electrical Engineering and Electronics by B. L. Thareja. Thank you.