 I, Mrs. Veena Sunil Patki, Assistant Professor, Department of Electronics Engineering, Vulturen Institute of Technology, Solaapur. Welcome you all for this session. At the end of this session, students can derive the relation between maximum value and RMS value of alternating current. So, in this session, we are going to discuss about the difference between AC and DC, voltage and current equations, instantaneous value, maximum value and RMS value. So, in this slide, you can see the alternating current, the graph is in between magnitude and time. The magnitude changes with respect to time, but in another diagram, you can see the magnitude remain constant with respect to time, that is called as the direct current. At any instant, at any time, the magnitude is constant, that's why that is called as the direct current. So, that is the difference between AC and DC. So, here let us see about the terms related to AC fundamentals in short. So, capital T is the time period. So, the time period is the time which is required to complete a one cycle. Here, you can see in this diagram, the VP is the peak amplitude or the peak value. So, this is the peak value that is also called as the maximum value, that is also called as the amplitude of the cycle. So, amplitude or the peak value is indicated by the VP or VM. So, this VPP is the peak to peak amplitude or peak to peak value and this is called as the frequency F equal to 1 by T. Frequency is the term which relates with the number of cycles completed in one second. So, that is measured in terms of hertz. One more term here is indicated that is the RMS value. This RMS value is indicated here, but what is the use of that RMS value? Why we use that RMS value? We have to discuss about that in detail. So, continuously the AC value changes its magnitude. We have to indicate that AC voltage by using a one term, one value. So, generally we use the RMS value to indicate that AC voltage. So, in India, the 50 hertz is the standard frequency and the 230 volt 50 hertz is the standard voltage which we use in our house. Pause the video and think about this. What is the standard voltage and frequency in India? So, in India standard voltage which is used for our home is 230 volt and frequency is the 50 hertz. So, the definition of RMS value is the RMS value of an alternating current is given by that steady current which when flowing through a given circuit for a given time produces the same heat as produced by the alternating current when flowing through the same circuit for the same time. It is also known as effective or virtual value of the alternating current. So, in other words, the RMS value is defined as the square root of means of squares of instantaneous values. But this is the definition. Let us discuss about this in detail. So, if we consider this is the resistive circuit, R is the resistance. So here first connect the AC voltage to this resistive circuit for which we have to measure the RMS value, connect that then the I current flows through that circuit. So, that will create the H heat in T seconds or T time in this circuit. So, measure that heat in time T. Now, replace this AC voltage for the same circuit. So, and again consider the same circuit, replace this AC voltage by a DC source and adjust that DC source like that H heat is produced in T time. Same heat as produced by AC is produced due to this DC. So, this is the DC or the steady state value, constant number we can indicate that. So, this constant value or the DC value is called as the RMS value of this AC. So, I DC is the current which create the heat H in the circuit in time T. So, H heat due to this DC is measured by H I DC square into RT according to Joule's law. So, this is the AC cycle, so AC cycle which is given by V equal to Vm sin omega t, this is the mathematical equation for the AC voltage or I is equal to Im sin omega t is the mathematical equation for this current where this graph. You can see here voltage or current you can consider here the n parts. If we make n parts here and if we measure the I1, I2, In, so here number of parts are In and if we measure the instantaneous heat or the instantaneous value which create the heat in the AC circuit when we apply the AC voltage to this resistive circuit. So, that instantaneous heat when we add for that whole AC cycle we can write down that H AC which is heat which heat create in the circuit is given by I1 square RT by n plus I2 square RT by n like that I n square RT by n. So, if we calculate that I1 square plus I2 square plus I n square divided by n into RT if we equate both heat because that is the definition according to definition both heat are equal. So, here if we equate that we can write down that as I dc square RT equal to I1 square plus I2 square plus I n square divided by n into RT. So, cancel out this so we will get here so I dc square equal to I1 square plus I2 square up to I n square divided by n. So, I dc equal to under root of this I1 square plus I2 square up to I n square divided by n. So, this is the squares mean you can see here squares addition divided by n is nothing but the squares mean but in this root that is why the name root mean square value is given to this term. Squares mean is in root. So, this is called as the IRMS. Here the IRMS equal to for this AC cycle what is the current equation I equal to I m sin omega t. To calculate the RMS value take the root of that equation take the integration for this for 0 to 2 pi and this I square d theta by 2 pi. So, put that I equal to I m sin omega t I m square sin square omega t or this omega t we can replace as a theta also. Here theta is nothing but omega t divided by 2 pi. So, consider this equation that is I m square by 2 pi. So, sin square theta is 1 minus cos 2 omega t. So, we have to consider here d omega t because theta is nothing but omega t divided by 2 is the formula for sin square omega t. So, if we calculate the integration of this. So, this is the 0 to 2 pi integration. So, I m square by 2 pi or here take that 2 common here. So, I m square by 2 pi or here integration of 1 is omega t or theta minus cos omega t integration is sin 2 omega t by 2 and limit is 0 to 2 pi. So, if we put here the limit for this equation we will get I m square by 4 pi into 2 pi only. So, here we will get under root I m square by 2. So, I RMS is given by I m divided by under root. So, here 1 by root 2 is nothing but 0.706. So, this is 7 into I m. So, this is the relation between I RMS and maximum value. If we know the mathematical equation that is I equal to I m sin omega t. If we know that from this we can calculate the RMS value. So, here omega is also given by 2 pi f. f is the frequency in hertz. So, you can refer the book Fundamentals of Electrical Engineering by B. L. Thareja. Thank you.