we are now going to shift our focus on the power analysis in case of AC circuits and we know already that the power calculation is the most important aspect of network theory and the first type of power we are going to have discussion on is instantaneous power the electric power at any instant of time is known as instantaneous power and there we measure instantaneous power in watts and we know already that the instantaneous power which we are representing by PT absorbed by an element is equal to the product of the instantaneous voltage VD across the element and the instantaneous current IIT through the element so if we have one element across which the voltages V T and current through the element is high T then the product of VD NID who will give us the instantaneous power PT and let us say that voltage VT is equal to VM cos Omega T plus theta sub V and the current I T is equal to I M cos Omega T plus theta sub I and therefore we can say that the instantaneous power PT will be equal to VM I am cos Omega T plus theta V multiplied 2 cos Omega T plus theta I now we will focus on cos Omega T plus theta V multiplied 2 cos Omega T plus theta hi we know 2 times cos a multiplied 2 cos B is equal to cos a minus B plus cos a plus B or we can say that cause a multiplied to cause B will be equal to one over two cos a minus B plus one over two cause a plus B and when you compare cos a cos B with this you will find Omega T plus theta B is a and Omega T plus theta I is B and therefore following this we can finally write down our average power PT equal to VM hi M over 2 cos theta B minus theta plus VM I M over 2 cos twice of Omega T plus theta B plus theta I so this is our average power and when you focus on this term you will find there is no time therefore this term is our time independent term and here you can see that we have twice of Omega and when you focus on the frequency here you will find V T and I T have the frequency Omega but in case of instantaneous power the frequency is twice of Omega so we can see that the instantaneous power will have twice of angular frequency as compared to voltage and current [Music] [Applause] [Music]