# Resistors in Electric Circuits (3 of 16) Voltage, Resistance & Current for Parallel Circuits

okay in today’s video I am going to go

over how to calculate and determine the resistance the current and the voltage

for simple parallel circuits. Okay this is the parallel circuit that we’re going

to use is the most common way a parallel circuit is drawn but there is more than

one way to draw them the important thing to notice here is that the voltage

source, our battery, and all of the resistors are parallel to each other and

they actually look like they’re each parallel to each other and that’s the

biggest hint that you have parallel components in a circuit when they look

like they’re parallel and they’re usually drawn correctly then it’s

probably a parallel circuit okay. Now these are the five things we’re going to

do first we’re going to get the total voltage gain in the circuit. Then we’re

going to get the equivalent resistance or the total resistance as i’d like to

call it in the circuit. Then the third thing is we’re going to get the total

current to the circui. Now these are the things I like to call kind of a big

three. We got to get these three things these totals taken care of

then we can figure out what the voltage drop is across each of the resistors and

then, we can figure out what the current is through each of the three resistors.

Now this circuit has three resistors all these rules apply whether you have two

resistors three resistors four resistors five it does not matter if you had only

one resistor it would actually be a series circuit but if you have more than

one resistor and all these rules that we’re going to talk about apply and

we’re going to start with the total voltage in the circuit. This is the

voltage gain this is the battery this is the thing that causes the electrons to

gain energy or to get potential electric potential energy there’s only one of

them so it’s pretty straightforward. The total voltage gain in the circuit is 20

volts and I like to put down here total because I know that’s my total

voltage gain. Okay now we’re going to do the equivalent resistance and this is

the tricky part. You remember in series circuits we just added them up this

would be seven fifteen plus twelve you cannot do that you know a parallel

circuit I know you want to because that’s the easy way out

but you have to use this scary-looking equation. Now it’s not that complicated

but yes to figure out the equivalent resistance you must use this equation

and this equation is simply not just adding them up ok so let’s go through

it’s 1 over RT which is the total resistance equals 1 over R1 plus 1 over

R2 plus one over R3 so we’re simply just going to first plug the numbers in now

it’s still just 1 over RT equals 1 over 7 ohms plus 1 over 15 plus 1 over 12

ohms now pick up your calculator and you can just punch these right into your

calculator like this ok it’s just simply 1 divided by 7 plus 1 divided by 15 plus

1 divided by 12 and that will give you what 1 over RT equals 1 over R T not

R T this is not the equivalent resistance this is 1 over RT is equal

to 0.293 Now in order to get RT I’m going to take the reciprocal of

this side and the reciprocal of this side if I take the reciprocal of this

side I just get RT if I take the reciprocal of this side I get 1 over 0.293 so in order to figure out what R T is I have to do on my

calculator 1 divided by 0.293 if I do 1 divided by 0.293

then I will get that the total resistance the equivalent resistance of

that circuit is 3.41 Ohms. Okay so it’s a little bit of math

not that complicated practice figure it out and you’ll get the steps down. Now

let’s get the total current once again we’re going to use Ohm’s law and in

order to use Ohm’s law we’re going to use the current so we want to solve for

I hi stands for the current this is the voltage this is the resistance we’re

going to divide each side by R and we’re going to get that the total current I

put down I tea because it’s the total which is

different than the current through each branch I want to make sure I keep those

things separate from each other. The total current is simply the total

voltage divided by the total resistance. Okay if I use the total voltage and the

total resistance I’ll get the total current. Okay so let’s

go through IT equals the total voltage is 20 we determined the total current

excuse me the total resistance is 3.41 and therefore the total

current is 5.87 amps now we have the total voltage the total resistance

and the total current and those are the first big 3 things we needed to figure

out for that circuit. Ok now we can get the voltage drop the voltage drop across

each resistor. Now we need to think about parallel circuits what is the voltage

rule the rule concerning the voltage drops well we talked earlier that the

rule is that the voltage drop across each resistor one two and three is equal

to the voltage gain from the battery all right so they’re all equal to each other.

Now let me just point out I’m trying to show you why let’s look at this resistor

between this resistor and the battery there really are no elements in the

circuit that are going to use any power or any energy. Yes this one is kind of

between it but if you follow this resistor back to the battery on both

sides back to the battery ok just take your fingers and put it on the diagram

there’s nothing between that resistor and the path back to the battery. So

there’s nothing that’s going to use any of the energy that would be delivered to

that resistor ok there was another resistor here or here or down below then

there would be something that would be using some of that energy but there’s

nothing between any of these resistors this one goes right back this one goes

right back so they all get the full power from the battery and that’s why

that works out like that. So if we want to know what the voltage drop is the

amount of energy used by resistor number one is just equal to the

voltage from the battery the total voltage 20 volts okay same thing for

number two and same thing for number three but each equal to the total

voltage or the voltage from the battery. Okay now that seems a little hard but

there if you think about it they’re really all just connected right back to

the battery okay now we’re going to go and do the fifth thing which is the

current through each resistor now we have to think about parallel circuits

what’s the rule for the current the current rule is that the current through

each branch, through each resistor. Branch 1, branch 2, branch 3. The current

through each branch is going to equal the total now we set earlier the total

is 5.87 amps that’s the current that comes out of this part

of the circuit comes out of the battery. Well you have to kind of think about it

a little bit conceptually right here at this point we call this a node and

there’s a split some of the current is going to go here the remainder of the

current is going to go here. There’s another node right here some of the

current is going to go this way and some of the current is going to continue

through and they will actually all come back and add up. So the total current is

the same here and here but through the branches it’s going to be different now

the branches there’s three branches each gets some of the current so when we add

them up you get the total. Now in order to calculate them we’re going to have to

use Ohm’s law again and we’re going to have to use those for the current now we

want to find the current to a number one so we have to get the voltage through

number one and divide that by the resistance of number one. This resistance,

not this resistant that’s why I like to write down I1 V1 R1. Okay if you want

I1 you have to use V1 and R1 V1 is 20 volts same as the total which we got

in the previous slide and this is R 1 is 7 and that’s 2.86 amps of

current through that branch now we have I2 we’re going to take V2

which is still 20 divided by R2 which is now 15 which is 15 and you get that the

current through the second branch is 1.34 you’ll notice the resistance is

higher, this is 7 this is 15 so this is going to be less okay and this is about

twice as high so this is twice as less or half as much. Okay, now the third one,

now of course this should say I3 but we have V3 and R3. V3 is 20 all the

voltages with drops are equal to the total this is 12 the resistance of the

third, 12 ohms and you get 1.67 amps, alright so there we’ve done

all three currents and let’s look back at our rule the current will set these

three currents should add up to the total well let’s see two point eight six

plus one point three four plus one point six seven those equal five point eight

seven so if they all add up then we know we have two pretty good feeling we did

that correctly all right. So once again we get the voltage the resistance the

current totals, then we got the voltage across each resistor, then we use the

current rule to get the current through each resistor along with Ohm’s law. Okay

so I know that’s five steps it’s kind of a lot the rules, the equations, write them

all down follow the steps, plug the values in get the answers with the

correct units. Think about your thinking to see if you get everything in the

right order everything makes sense and I think you can do those problems no

problem. Ok thank you for watching and if you enjoyed that video or found it

helpful please leave me a thumbs up or give me a

comment in the comment section below thank you very much