# 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