MCAT Physics Circuits: Current, Resistance, Capacitance & Measurement

hi everyone today we're going over chapter six of physics for the mcat which covers circuits

chapter 6.1 is about current which is defined as the movement of positive charges however we know now

that um current is actually caused by the movement of electrons which are negative

charges so if you see current going in a specific direction just know that the

electrons are actually moving in the opposite direction a useful concept is that of conductivity

which is just how much current can this material conduct and this is in units of siemens

also known as s or one over ohms the reason why this is important is because um ohms is the unit for

resistance which is just the opposite of conductivity it's the ability to resist

a current from flowing and so it's pretty intuitive that conductivity would be the reciprocal of um resistance

there are two main types of conductivity there's metallic conductivity which is just the conductivity of a

metal metals are usually described as a sea of electrons

because all of the atoms in the metal are effectively sharing all of the electrons and the electrons

are fairly free-flowing which is why metals are so conductive because

the electrons can flow from one side to the other really easily the other type of conductivity is known

as electrolytic conductivity um electrolytic conductivity is when ions are dissolved

in a certain solution and the ions themselves have charges and so they're the ones that will be moving

around to create a current or a movement of charge

and this type of conductivity is concentration based so for example if you dissolved nacl

which is table salt into a cup of water the more salt that you dissolve

the more conductive the solution will be which makes sense because the more um nacl you dissolve the more

positive and negative charges you have that are able to move around and create a current so current is

um denoted with the letter capital i and it is defined as q over delta t where q is the amount of charge and

delta t is time so current is defined as how many charges are moving past a certain point

over a certain amount of time and this is in units of amps so there are two types of currents

one is called direct current which is just current moving in one direction and the other is called alternating

current so alternating current is actually what most of our um appliances use now

however the mcat will not focus on alternating current we'll only be talking about direct current to make

things easier so another concept that's useful is the

idea of potential difference so we discussed in the last chapter what a volt

is and this is a really really important concept in this chapter um so a potential

difference is also known as the electron motive force denoted by these things um but it is also what's

known as voltage so voltage is the same thing as potential difference

which means that if you have two points in space and one has a higher potential and the

other has a lower potential then your charged particle is going to want to move from the higher potential

to the lower potential and so i like to think of voltage as a kind

of potential energy um kind of like if you raise an object off the ground and now it has more potential energy

and wants to fall toward earth um this is how i think about voltage as well and so volt als though it's called

electron motive force voltage is not a real type of um force it's actually a measure of kind of potential energy so

now that we know these things we can talk about some of the rules that govern circuits

so our first rule is going to be kirchhoff's junction rule so all this rule means is that the

amount of current that goes into a junction is the same as the amount of current going outside

going out of the junction so if you look at this junction that i drew here um there's more to the

circuit i just didn't draw all of it so if we have this one path going in let's say that this one path is

maybe 5 amps then we know that the amount going in is the same as the amount going out so the other two

branches if this one was three amps then this one must be

two amps and um that's all there is to the junction rule and it makes intuitive sense if you have

five charges going in you have to have five charges going back out the next rule is the loop rule

so all circuits are going to be loops and so if you look at the circuit that i drew here first of all this

um the symbol over here is how you denote a battery typically the long side will be the

positive side and the short side will be the negative side um but a battery has to have a positive

and a negative side and what a battery does is that it drives all of the charges in a circuit

from one side to the other side so in this case this is the positive side and so there are no charges on

there are no electrons on that side and the side is the negative side which means that

all the electrons are built up on the side and so this gives the positive side of

the battery a um very high uh voltage and the negative side of the battery

a much lower voltage and so all that the loop rule means is that when we go around this loop

um all of these 10 volts have to be accounted for somewhere because you you don't just change

voltage for no reason so when we go around the circuit we can see that we have two

of these squiggly line things these squiggly line things are what are known as resistors and

resistors cause um voltage to be dissipated so when we go around this loop we can say

that at the first resistor maybe we lose 5 volts or we have a voltage drop

of 5 volts and at the second resistor we also drop 5 volts and so the loop rule just says that

everything has to be accounted for so if we start here at 10 volts then we lose 5 volts and then we lose

another 5 volts then that makes sense so when we get back here we have zero volts

chapter 6.2 is about resistance and you can calculate resistance with this equation it's going to be in units of

ohms and so resistance is defined by rho this row is going to be a constant

it's called the resistivity and this is going to be a different constant for every kind of material

l is the length of your resistor so if you think of a resistor as kind of like a filter then the longer

this filter is the more distance it has to filter stuff out and so

the longer it is the more resistant it will be and this is divided by area so if you

think about it once again as a filter then the wider this filter is the more charge is going to be able to go through

it at any given time and so the bigger the area then the less resistance something has

and the most important equation in this entire chapter i think is ohm's law and ohm's law is

equal to v equal to ir where v is voltage i is current and r is resistance and this

equation governs basically all of circuits and you need to know this equation it

might be more intuitive to think about it as i which is current equals voltage over

resistance um it might be more helpful to think about it this way because current will be bigger if the voltage is

bigger and current will be smaller if the resistance is bigger um but v equals i are very very important

and another equation that's kind of helpful is power so in circuits we think about power not

as um like doing something but we think of it more in the context of power that is

dissipated and power that is dissipated specifically by a resistor

so we talked about in this picture up here that um this resistor is basically causing a voltage drop of 5

volts and so if it's taking away voltage then it has to dissipate power

and so in circuits power is defined as p equals iv um there are some obscene mnemonics to

remember this and this is also equal to i squared equals r which we can find simply by

plugging in v equals ir to p equals iv a harmonic for this is twinkle twinkle

little star p equals i squared r and this is also equal to

v squared over r but you can find both of these other forms just by plugging in v equals ir

to p equals iv and this is how you find how much power is dissipated by each resistor

so if we're looking at our circuit above we can plug in the current which i didn't give you for the circuit

and then the voltage here we're going to look at what's going to happen if you have multiple resistors

in the same circuit and the difference between resistors in series and resistors in parallel

is another very important distinction in this chapter so first off a resistance in series is

when you have the multiple resistors just lined up in a row such that

if you had a charge then this charge must go through all of the resistors in order to get to

the other side resistance in parallel means that if you have a charge

um over here wanting to get to the other side you can choose any path so you can choose to go through

r1 r2 or r3 um it's not important here that i drew

resistor one closest to the um entrance and the exit of this circuit part

you can draw these anywhere um the only important part is that your charges can choose to go through

um r1 r2 or r3 and so if you have a resistor if you have resistors in series um we

can think about the equation v equals ir and we know that um current we know that current is going to

be constant throughout this entire circuit because if you have a charge or if you

have three charges over here on the other side you're always going to end up with three charges

um so we can just ignore this i term for now and if we think about the voltage drops

so the total voltage drop for resistors in series is going to be that the total voltage

drop is equal to all of the voltage drops added together and this is because

if you have a voltage drop of let's say two volts here one volt here and

two volts here then the total then the total voltage drop will um be the sum of all of these

because your charge is going to have to go through each and every one of these to get to the other side

um and so it follows that the total resistance is going to be also all of the resistances added

together following the equation v equals ir and so um this is really important if let's say

you had a question that said um the resistance of r1 is going to be 3 ohms and of r2

it's going to be 2 ohms and of r3 it's going to be 1 ohm then it wants to know the total

resistance of the circuit then you would just add them all up and you would say that the total resistance

is going to be equal to 6 ohms you can also do this if it tells you the voltage drop of each

resistor or if it tells you the total voltage drop and asks you to go back and find

the voltage drops of each individual resistor so it gets a little bit more complicated

with when we think about resistors in parallel um so first off if we want to think about the voltage drops of

resistors in parallel we can think that the voltage drop of v1 um which is the drop of r1 is

the same as for r2 and it's the same as for r3 so we're not going to be adding them together

we're going to say that they're equal to each other and this is because let's say that the voltage up here is 8

volts and the voltage down here is 4 volts then that means no matter which path the

charge took it had a voltage drop of 4 volts so r3 is going to have a voltage drop of

4 volts so is r2 and so is r1 um because the charge only takes one of the paths

to get from one side to another and then um the second equation which is that the total resistance or

rather the reciprocal of the total resistance is equal to the reciprocal of each individual

resistor and if you think about this a little what this means is that the more

resistors you add um the less resistance you actually have which makes a lot of sense actually

because if you think about resistors as um like blocking the current then if you add more paths so

if you only had r1 here then all of your charges can only go through r1 which will slow them down

significantly but then if you add two more resistors that's two more paths your charge can go down

which means that there's actually less resistance even though there are more resistors

and so these equations are also similarly useful so like if you were given the

resistances of each individual resistor and asked to add them all up together into a total um another way these

equations can be used is let's say i'm drawing a hypothetical circuit

where here we have one resistor r1 and here we have r2 and here we have

r3 and we have current going kind of this way this is not how you draw circuit

notation you wouldn't put an arrow here um i'm just adding it for clarity and so if we wanted to know um the total

resistance of this entire circuit element then we would first want to add up

r2 and r3 in parallel and we know they're in parallel because when once you get here you can either

choose to go this way or that way um and so we would add them up using that the total resistance i'm going to

call this r4 is equal to 1 over r2 plus 1 over r3 or this is 1 over

r4 sorry um and then we can go and redraw the circuit because we've now added r2 and r3

together so now we have r1 and r4 and r1 and r4 are now in series with

each other and so then we can add up the total resistance of

this entire circuit element is equal to r1 plus r4 and that's one of the ways that you

would use all of these equations chapter 6.3 is about capacitance and capacitors

so capacitance is just the ability for anything to hold a charge um capacitance is calculated with this

equation where c is the capacitance of a particular capacitor

and it's equal to q which is charge over v which is voltage so what this means is

that if you have something with a capacitance of say one ferad a ferrite is the unit of a

capacitor and your entire circuit has a voltage of let's say five then you're going to be

able to um hold five charges in your capacitor but let's say your voltage is now 15

um because the voltage of a circuit can change based on the battery so if you now add a

stronger battery this capacitor is now going to be able to hold more charge

so capacitance is the measure of how many charges it can hold per voltage of the circuit and not a

direct measure of how many charges it can hold and a ferret is in units of

c which is coulombs this is not capacitance this is coulombs over volts because coulombs is the unit

for charge so capacitors are drawn um this way with two parallel lines

this looks kind of like a battery but don't get this confused with a battery a battery will always have one short

line and one long line another difference between um a capacitor

and a battery is that a capacitor has to be charged by a battery um and a capacitor can only hold charge

for a very limited amount of time a capacitor doesn't have energy on its own the

um only ability of a capacitor is to hold charges away from each other

and also always in a capacitor the um charge of the negative side has to be equal to the positive side

so if the side is let's say five if you have five charges here then you have to have negative five

here and this is because in order for this to happen um all of the charges must be driven

from the negative side to the positive side and then

so therefore the negative side will have the same amount of deficiency of charge that the positive side

has charge if that didn't make sense don't worry this is not very important what's important is this equation here

so capacitance can also be calculated as e naught which is this constant here um you'll be given

this constant don't worry about remembering it and multiplied by the area of the

capacitor so this is multiplied by area because the larger the area of your capacitor

plate um the more charge it can hold and this is divided by the distance between the

plates so the closer together your plates are the higher the capacitance and this is

because each plate has its own electric field and so the closer um the plates are the more

the the stronger the fields will be um yeah so these are the two equations you would use to calculate capacitance

um another concept is that of a dielectric material um which is also known as an insulator

so this equation here um c prime which is your new altered capacitance as a result of the

dielectric oh so dielectric material is one you can place

in the middle of your capacitor and this alters the capacitance of your capacitor because

essentially the dielectric takes up a bunch of the free space here and so it effectively brings the

capacitors closer together because there's less space between

and so the new altered capacitance is going to be equal to k which is a constant multiplied by the original

capacitance and so this k will always be greater than 1 which means your new

altered capacitance will always be greater than the old one um if it was less than one then it

wouldn't be a dielectric material anymore i forgot to mention this so

the potential energy that's stored in a capacitor is equal to u equals one half

c v squared where c is the capacitance and v squared is the voltage so i think of this

kind of like the equation one equals m v squared that's just how i remember it um where

mass is kind of like capacitance and velocity is kind of like voltage this always made sense to me

similar to four resistors we can also have capacitors in series and in parallel

but these equations are going to be the opposite of those seen for resistors and so to understand why this makes

sense we can look at the equation that we wrote for capacitance which is e naught which is a constant

multiplied by area over a distance and so when we look at capacitors in series which means that if

you had a charge it would go through all three of these capacitors um effectively what is going to happen is

that this charge is going to have to go through three separate distances um there's

going to be d1 d2 and d3 so we have to add up all of these distances

and as we can see in this equation the greater the total distance the less the total capacitance which is

why we use this equation which means that the more capacitors you add in series

the less capac the less total capacitance there is going to be um and if we think about the situation

in parallel which in resistors we used the um this equation of reciprocals

when we look at capacitors we're going to just add them all up and this is because if you had a charge

and it can choose to go through each of the paths then it's only going to go through one distance so this

distance term is unchanged however you have a situation where charge can build up on each of these plates

which means actually if you have three capacitors then three times the charge can be built up and therefore we have a

case where the capacitance equals all of the individual capacitances added together

if you're wondering why we can't also add up the areas in the case of capacitors in series we

can think back to our equation c equals q over v um where v is voltage and q is the

amount of charge and so if we think that for both of these series

if for both of these systems of capacitors that we have a voltage drop of three

which means that up here we have three volts and down here we have zero volts this means that in the case in parallel

each of these capacitors is going to have a voltage drop of three so far capacitance is 1

then we can have 3 q or q is in units of coulombs over 3 volts

which gives us more charge but on the other hand in series we're going to have three

separate voltage drops so each voltage drop if we have a capacitance of one

is going to be one coulomb over one volt and so that's why even though they're in series

it doesn't mean they're going to be able to hold more charge chapter 6.4 is about meters

which are all the different devices that you can use to measure your components of a circuit

this is pretty straightforward an ammeter measures current in amps a volt meter measures

voltage drops in volts and for both an ammeter and a volt meter you're going to want to turn

your circuit on because you can't measure current unless the circuit is running

and you also can't measure a voltage drop unless your circuit is running because if your circuit isn't running

then there is going to be no voltage drop for an ohmmeter it measures resistance

in ohms and for an ohmmeter your circuit should be off

because for an ohmmeter your ohmmeter is going to run its own current through the resistor to find out how much

resistivity there is and so thank you so much for watching i hope that this video helped you out

and yeah see you in the next chapter