 I am Mrs. Veena Sunil Patki, Assistant Professor, Department of Electronics Engineering, Valshan Institute of Technology, Solapur. Welcome you for this session. At the end of this session, student can derive the relation between maximum value and average value of alternating current. Definition of average value is the average value of an alternating current is expressed by that steady current which transfers across any circuit the same charge as is transferred by that alternating current during the same time. In case of symmetrical alternating current, the average value over a complete cycle is 0. Now, consider this resistive circuit, connect the AC voltage to that circuit for which we want to measure the average value. So, this is the AC voltage V equal to Vm sin omega t. Connect that voltage to this resistive circuit. I current flows through this, I is given by I m sin omega t. So, when this I current flows through this circuit, Q charges move through the circuit in time t. So, we have to measure this Q charges in time t. Now, replace this AC voltage, the same circuit is considered here, replace this AC voltage by a DC source by the DC voltage to the same circuit. I current flows through that circuit, I dc, we can consider that I dc again measure the Q charges move in the circuit in time t seconds. This Q charges move in time t will be same for AC and DC. So, this voltage we have to adjust. So, this DC voltage is the average value of this AC voltage. So, according to this definition, this DC voltage is nothing, but the average value of this AC voltage. Now, consider the half cycle of AC cycle, make the n parts of that cycle voltage or current, we are going to consider for that. So, I 1, I 2 and I n are the parts of this half cycle. If we calculate the average of that, that is I average equal to I 1 plus I 2 plus I n divided by n is the average of this half cycle. But if we calculate the average of negative cycle, that will be negative of that half cycle. So, total average of this cycle is 0. So, average value for whole AC cycle is 0. Now, if we want to calculate the average value for AC cycle by analytical method. So, this is the graphical method. So, by analytical method, we are going to consider the value I equal to I m sin omega t. This is the mathematical equation for the current, where I is the instantaneous current, I m is the maximum current and omega t is the theta, where omega is the angular frequency that is given by 2 pi f. So, I average according to definition 0 to pi. Here, we are going to calculate the average value for only half cycle 0 to pi I d omega t. So, put the value of I as I m sin omega t 0 to pi I m sin omega t, but we have to calculate the average. So, I by pi is the average value, so d omega t. So, here we will get the equation as I m by pi 0 to pi sin omega t d omega t. So, here I m by pi integration of sin omega t is minus cos omega t 0 to pi. If we put the limit for this equation, we will get I m by pi minus cos pi plus cos 0 that is equal to I m by pi into 2. So, 2 I m by pi is the I average value, so I average is given by 2 I m by pi. So, if we calculate 2 by pi, we will get the value as 0.637 I m, so this is the average value 0.637 I m, this is the relation between maximum value and the average value of the AC cycle. Now, what is the importance of this average value here? When we convert the AC voltage to DC by using rectifiers, we have to consider this average value, this average value is nothing but the DC value of the AC cycle. So, we can consider this relation to calculate the average value, so here now pause the video and think about what is the average value of whole cycle, average value of AC cycle is 0. So, form factor is the ratio of RMS value to the average value, RMS value is 0.707 I m, average value is given by 0.637 I m, so the form factor is given as 1.11, so that is the constant value and for AC cycle, AC sinusoidal cycle, this form factor is constant and the knowledge of form factor will enable the RMS value to be found from the arithmetic mean value and the importance of form factor is, when we derive the formula for transformer, we can use this form factor, so in some applications we can use this constant value 1.11 to calculate the RMS value if we know the average value, directly we can calculate the RMS value, so here the next term is the peak or amplitude factor or the creased factor, this is also the ratio between maximum value and RMS value, so I m divided by I m by root 2, so that is equal to root 2 and that will give you the value 1.414, it is also the constant value and the knowledge of this factor is of importance in dielectric insulation testing, because the dielectric stress to which the insulation is subjected is proportional to the maximum or peak value of applied voltage, the knowledge is also necessary when measuring iron losses, because the iron loss depends on the value of maximum flux, which is present in magnetic circuit. So, when we consider any magnetic circuit, this amplitude factor is important for that, you can refer the book Fundamentals of Electrical Engineering and Electronics by B. L. Thereseja, thank you.