 Welcome to this session. I am Priyanka Bidla, assistant professor in electronics and telecommunication engineering. Today we will solve the numerical on AC fundamentals. These are the learning outcomes of this video lecture. At the end of this session students will be able to explain the fundamentals of AC circuit and students will be able to solve numerical on AC fundamentals. These are the contents of this video lecture. Now before moving towards pause this video for few seconds and you have to recall the terms related to AC fundamentals and with the help of that we have to solve the examples. Now pause this video for few seconds and you have to recall. So this is AC signal. Here we have to find some definitions. So first one cycle. So we will see some here this is a AC signal and now we will see some definitions related to AC fundamentals. First upon cycle, so one complete cycle or one complete set of positive and negative values of the alternating quantity is known as the cycle. Then time period, so time period is nothing but the time taken by the alternating quantity to complete the one cycle. So time is always measured in the second or we can write down t is equal to 1 upon f then frequency. So frequency is nothing but the number of cycles per second and its unit is hertz it is denoted by f or we can say f is equal to 1 upon t also. Then the next parameter that is amplitude. So the maximum amplitude the maximum now next term is amplitude the maximum value positive or negative of an alternating quantity is called amplitude. Then angular frequency. So angular frequency is represented by omega and it is also called as angular velocity. So it is the angular distance covered in one second. Omega is equal to 2 pi f or we can say 2 pi upon t and its unit is radian per second. Then the next term instantaneous value that is represented by small i. So value at any instance is called instantaneous value. So the equation for this is i is equal to i m maximum current into sin omega t. Now with the help of this we will try to solve the example based on the AC fundamentals. So here first example in the first example this is signal is given and the alternating current that is for the frequency 60 hertz is given and has the maximum value of the current is 120 ampere that is i m is given and the frequency is given. Now we want to find out these terms. So here maximum value of current is given that is 120 ampere and frequency also given 60 hertz. Instantaneous value of i is given by how to find out this is i is equal to i m sin omega t. So put the values into that and we are getting 120 sin 2 pi into 60 into t. So here small i that is instantaneous value of current i is equal to 120 sin of 120 pi t. Now second question, reconning time from the instant current is 0 and becoming positive since point O has been taken as a reference. So here this is the point O has been taken as a reference and i is given. So i is equal to 120 sin 120 pi t. Now for this example t is given, time is given that is 1 upon 360 seconds. So here you have to put into this equation and after solving this we are getting i is equal to 120 sin pi of pi by 3. So you have to calculate and we will get the answer i is equal to 103.92 ampere. Then third point, suppose the current becomes 96 ampere for the first time after t seconds. So here after t seconds the time means for after 6 seconds the current is 96 ampere. So at this instant how to calculate i is equal to i m sin omega t. So i small i instantaneous value of the current is given that is 96 ampere. So 96 is equal to 120 sin 120 pi t, t is given yes 1 upon 360 seconds. So you have to put the values into that and we will get sin inverse of 0.8 is equal to 120 pi t. Again you have to calculate 0.927 radian is equal to 120 pi t and finally we get the time that is 0.00246 second. This is the answer of the third question. Now we will solve the second example and alternating current is given by this is given i is equal to 10 sin 942 t. Determine the time taken from t is equal to 0 for the current to reach a value at plus 6 ampere for first and then for the second time. So we want to calculate the time for first 6 seconds for first 6 ampere and then for second this one. Now we will solve this one. Let the current become plus 6 ampere for the first time for the first t second. So i is equal to i m sin omega t. So this instantaneous value is given 6 ampere. So 6 is equal to i m is also given 10 sin 942 t. 6 upon 10 is equal to sin 942 t. So t is equal to 942 t is equal to 0.643 radian. So after doing the calculation we will get the time t is equal to 0.68 millisecond. So here for first 6 ampere current means for this one time is 0.68 millisecond. So here let the current become 6 ampere for the first time after 0.68 millisecond. So here we require the time 0.68 millisecond. Now we want to calculate the frequency of the current that is omega is equal to 2 pi f. So f is equal to omega upon 2 pi then omega is given 942. So 942 upon 2 pi will get the 150 hertz. Now we want to calculate the time period of the signal. So here t is equal to what 1 upon f put the values of frequency here 1 upon 150 and here we are getting t is equal to 6.66 millisecond. So here this is the time. So you can see this is the whole time means here it starting from this point end width here. So we require the total time for this is what 6.66 millisecond. Now our question is what we want to find out the time taken to reach for the second time. For this second time we want to calculate the time. So here how to calculate? So time taken to reach for the first time plus time period. Yes in this way you can calculate. So time taken to reach for the first time is what already we have calculated that is 0.68 plus time period actual time period we require that is 6.66. So here you can see total time is what for this it is 6.66 millisecond and for this instant we have calculated 0.68 millisecond. So you have to add these two times and we are getting t is equal to 7.34 millisecond and the total time is what it is 7.34 millisecond. These are the references of this video lecture. Thank you.