in this video i'm going to analyze this ac circuit to determine the voltage across and the current through every component now this is a circuit with a combination of parallel and series components so there will be a few more steps in this circuit analysis than there were with the purely series and purely parallel circuits the general strategy that i'm going to take is to start by combining components to create an equivalent circuit and continue combining components until circuit is one equivalent component then calculate voltage and current for the circuit with one equivalent component and then finally expand the circuit back out calculating voltage and current for the components or the groups of components as i go until i've done this for every component in the circuit so more specifically to the circuit that i'm analyzing i'm going to start by determining the impedances of each of the components here then begin combining components to create equivalent circuits so to start i will take this inductor and capacitor combine them together to create this equivalent circuit then take these two components combine them together to create this equivalent circuit then combine these two components together to create this equivalent circuit with a single equivalent impedance then i can calculate the current in the circuit and use that information to go back to the previous equivalent circuit to calculate voltage and currents and continue until i am back to the original circuit and have all the voltages and currents calculated now here we are with the circuit and i'll start by calculating the impedances of all the components now i should note that for some of the calculations i am going to fast forward through them so if you need to see exactly what i'm doing for each step then you can pause the video whenever you need to okay let's start with the capacitor the reactance of the capacitor capacitor 1 is 1 over 2 pi fc the reactance of capacitor 2 has the same equation but it is a 1.5 microfarad capacitor and the reactance of the inductor is 2 pi f l frequency of 60 hertz inductance of 650 millihenries and now i can take all of these reactances and write them out as impedances so include the phase shifts that the components will introduce and now i'll do the calculation for the first equivalent circuit so this is combining these two components together to give me this equivalent component so that zl1 or zl1 plus z2 that's equal to j 245.04 ohms minus j 1768.4 ohms so the effect of adding the impedance of the inductor plus the impedance of the capacitor gives us something that looks like a capacitor because it's introducing this phase angle of minus 90 degrees or it's got a negative j component the next thing to do is combine these two components together into this one equivalent component so we've got r2 in parallel with the series combination of of inductor 1 and capacitor 2. now i'll convert this value that's in rectangular coordinates into polar coordinates i won't go through all the steps i'm just going to give you the value and then take the inverse of that number to give me the final impedance now finally let's make this third equivalent circuit where we have reduced the circuit down to one equivalent impedance by adding this capacitor one the impedance of capacitor 1 to this combined impedance that we've just calculated okay now we've got that total impedance calculated and we've got it shown here in rectangular as well as polar coordinates and now that we have the total impedance calculated we can now calculate the total current now working backwards from this third equivalent circuit to the second equivalent circuit i t goes through both of these components so we can use that i t value to calculate the voltage across capacitor one as well as the voltage across this combination of components here so that calculation is the current through capacitor one times the impedance of capacitor one and in rectangular coordinates that is and we can do the same basic calculation for the voltage across this combination of components the value that i need now going back a step from this second equivalent circuit to this first equivalent circuit is the voltage across this combination of components the combination of r1 in parallel with l1 plus c2 and since those components are in parallel the voltage that i've just calculated here is the same as the voltage across l1 plus c2 as well as the voltage across resistor two although i just noticed now that that should be resistor one shouldn't it so i can use that voltage to calculate the current through each one of these two components so that is that current there next i can calculate this current here so that like i said that should be r1 so it's the same voltage divided by the impedance of the resistor now the last two values that i need are the voltage across inductor 1 and the voltage across capacitor 2 and i can use this current that i've just calculated along with the impedance of capacitor 2 and inductor 1 to calculate those voltages and then i'm done and the voltage across the capacitor same calculation current times the impedance of the capacitor and that's it that was the last calculation now here's the table with all the values so in the table we have the voltages the currents and the impedances for all of the components c1 the inductor c2 the resistor as well as the totals now this table and example problem came from a free open source textbook and you can find the link to the problem in the description that website covers ac circuits dc circuits communication systems and if you're lucky enough to be viewing this video far enough into the future from when i created it it will also cover electronic circuits and digital electronics too as always thank you so much for watching i'll see you in the next video