funding for audible pain course television was made possible in part by the College Board almost nobody can reason with you Mr we's Cunningham McHugh the great founder himself and all other funding were made possible by viewers like you we forced you no God no God please no no hello and welcome back to another episode of the AP pctv the EM Edition I'm your host mq and today you'll be watching season one electric circuits episode 4 waxon kiro's logs so the objectives for today's video is you will to Define kir chops to laws for a circuit and and apply them to a circuit so kiro's laws they deal with the potential difference and the current in a circuit the first law or the first rule called Loop rule deals with the total potential in a circuit and that says the total potential difference around a closed loop which could be a circuit but any closed loop is 0 volts so if you sum together all the potential difference you get no volts of potential difference across that Loop the second rule is Junction rule which states that the total current going into or entering a junction is the same as the total current coming out of the junction or you could say the sum of I in total amount of current going in equals the sum of I out or the total amount of current coming out all right so all the two rules State total potential in a loop is zero total current going into a junction or where two wires meet is equal to the amount of current going out of that same Junction so Loop rule a simple version of loop rule we can take a look at a series circuit so in this series circuit we have a battery with some total voltage VT connected in series with R1 R2 and R3 three resistors so what you do for Loop rule is you whip out your pencil or your finger or your pen and you follow a circular path or a loop and what you do is you say the sum of the volts of that Loop is zero so this total Loop gives you potential difference of zero equals let me tell you some key rules on how you set up the equals part if you hit a battery going from through negative to positive like you conventionally should then leave it positive so we just have VT right if I go around this loop I hit the negative side first then come out the positive so if you hit a battery or a cell and you hit the negative side first and come out the positive side we're going to call that positive so that's sum of the voltages at zero is equal to Total voltage and then we hit resistor one which we know has a potential drop right resistors create potential drops we know this creates a potential drop how we handle this is is if it hits in the same direction as our current right our Loop goes clockwise our current goes clockwise then we subtract the voltage of the resistor so minus V1 if for example our current went counterclockwise but our Loop went clockwise you would add the voltage so if you hit the resistor the right way meaning your finger and the current line up you subtract the potential difference across the resistor so minus V1 you keep going you subtract V2 you keep going you subtract the voltage across resistor 3 V3 and so you've now completed the setup of your Loop rule you know the sum of the volts potential difference is zero is equal to VT minus V1 - V V2 minus V3 you hit everything how you're supposed to you H the battery negative to positive and you hit the resistors in the same direction as your current we can now manipulate manipulate this to say that total voltage is V1 plus V2 plus V3 and that's interesting that uh I would say that or one would say that because that is the exact rule for a series circuit so you have proven using Loop rule why total voltage adds in a series circuit it's because of loop rule because of loop rule the total potential difference has to be zero in this Loop this Loop happens to be in series a complete series circuit so if you actually just move all your V1 V2 and v3s over you get V total is V1 plus V2 plus V3 now what becomes extremely convenient is we can say that V1 is the current time R1 because V is IR we could say V2 is the current times R2 and we can say V3 is the current times are three and it might not seem convenient in the moment but the reason we can do this and we want to do this is a lot of times you want to solve for a variable you don't know maybe that variable is current I don't know in this case we're just plugging in variables but maybe you want to solve for current now you conveniently can pull that out and solve for it so just be mindful with with Loop Rule and kir laws that you can conveniently say voltage is current times resistance just pay attention to the current resistance you're using all right a little bit more sophisticated use of loop rules may be in this combination circuit where you have a battery R1 and R2 and R3 in parallel and this is a little bit more complex of a loop rule demonstration cuz if you take a finger and you follow the path you can't hit everything in one Loop that means the circuit has multiple loops and that's okay we just have to Define different Loops so let's take a journey I'm going to take my finger and I'm going to follow this inner loop right and I'm going to call that inner loop a I know this inner loop that it contains the battery R1 and R2 has a total potential difference of zero that's what Loop rule states and if I take it a step further I know well I hit the battery going from NE the positive so that's equal to VT I hit the resistance in the same way as my current so minus V1 and I hit resistor 2 with my finger in the same way as my current so minus V2 all right and now we've set up the loop rule for Loop a you could then take a step further and say well the current of loop a times the resistance of one is equal to uh V1 and that the current of a * resistant 2 is equal to uh V2 you could do that as well great but we don't need to take it that step per se but it's always important to recognize that V is IR we can then go through a second Loop right and we hit on this Loop the battery negative to positive we hit R1 in the same direction as the current and R3 in the same direction as the current so we could say is the sum of the potential differences is zero is equal to VT minus V1 minus V3 all right and what we can do is say then the total voltage is equal to I a * R1 plus ibtimes R3 or that current in this second Loop that other loop over there all right if we substitute out V equal ir and now you might ask why would we do this again it becomes down to potentially having to solve for a variable using systems of equations which I will show you right now so Loop rule especially in the scenario I just showed becomes particularly useful if you combine it with its friend Junction rle where current in equals current out so this only applies to Junctions I mean applies to every circuit but it really applies to parallel circuits almost more than any because you actually have a junction right where you split and your finger has to now go different directions so we're going to have the same circuit we just had in the combination example with R1 R2 and R3 R2 and R3 being in parallel R1 being in series with that and you have a current coming out of this battery let's call it i1 and it hits the junction so current in total current in is i1 but total current out is going to be I2 plus I3 why because it has a choice meaning the current now has a choice to go down through R2 or around through R3 now intuition tells you that the resistance with the Lesser value will draw more current which is fine but either way I2 + I3 the current coming out of that Junction or meeting point where your current splits is equal to i1 or what went into it all right that's all Junction R States whatever you got coming in current wise is whatever you got coming out all right and now if we put it all together with the same circuit with R1 r R2 and R3 you can now combine your Loop rules and Junction rules meaning your Loop rules are still the same you still have Loop a here right so you still have the sum of the voltages is zero in Loop a is V total minus V1 minus V2 or VT is i1 R1 plus I I'll just put I now R2 you now get the second Loop B is some of voltage zero is voltage of the battery minus voltage across that resistor uh one minus voltage across three and so you could say VT = i1 R1 plus I3 R3 and what happens is you might have multiple unknowns you might have up to three unknowns here so you need us do a system of equations combining your Junction rule where you know that I in or i1 equal I2 + I3 and which means I2 going through R2 and I3 going through R3 all right so what ends up happening is maybe you can substitute in equation three into equation two solve for I I2 and maybe put it into equation one but point being is it becomes an algebraic I don't want to say nightmare but becomes an algebraic challenge right but it's very important you can at least set it up the algebra part will practice that but you have to be able to know to set up a loop rule that sum of the voltages is zero and you need to know Junction rule that what goes in must come out in terms of current and then once you have these equations if the problem requires it based on um algebraic necessity you could do system of equations and solve for unknown variables this really if you did all this algebra would be if the verb chart fails you like if if you do the verb chart and there's just not enough information use a verp chart you would do a a system of equations with Loop Rule and Junction rule so if you have any comments or questions please leave a comment or email me otherwise guys have a fantastic night