what's going on my friends this is dustin stelzer with electricianu
today i'm going to answer a question that i had on instagram zack palecki he asked hey
dustin i had a quick question can you help me understand something our class was reading up on
ohm's law and our book was saying that voltage and amperage are directly proportional to each other
and resistance is inversely proportional to current does that mean if voltage increases
so will amperage i just didn't know if i was translating it correctly that's a really good
question so inversely proportional and directly proportional directly proportional means if you
raise one value the other one goes up directly with it inversely means if you raise one value the
other one's going to go down they're the inverse of each other so let's look at that a little bit
so we've got our ohm's law right so e equals i times r is ohm's law if we go back here this
is the wheel that we kind of use visually to to not have to worry about the craziness of the math
it's not that crazy but it helps people if you're trying to solve for i you know that your formula
is going to be i equals e over r you just hide the value you're trying to find resistance you
hide r and say r equals e over i same thing here if you're trying to find voltage you go e
equals i times r they're right across from each other so another way to look at that is just this
um i've rearranged all three of the equations it's the same things i was just showing you um so e
equals i times r but i also equals e over r and r equals e over e and if you don't know how to
like do that if that kind of blows your mind like why how how the hell if you just in basic
algebra if we have e equals i times r well this is solving for e so we need to know e
uh i and r but if we don't have the values and we need to solve for amperage instead
all you do is divide by whichever uh value that you're not trying to find so if we're trying to
find i we would divide by r to get rid of those r's and leave i isolated by itself but in the
equation you have to balance the equation so you always have to have whatever you do on the
left you got to do on the right so we would go e over r so that leaves us with i equals e over r
same thing you know we just do the inverse of it but that's how the math actually works out so if
you're ever sitting there in a test or in a class and you're trying to figure out like damn it what
was the formula i know this one but i don't know how to make it like that just remember
that you're dividing by the the value that you're trying to get rid of on both sides so if we have a
circuit and we know uh we took our multimeter out we tested the resistance of this certain resistor
and we didn't want to turn current on we wanted to know what kind of current we should expect
we know we have 120 volt circuit so we have our voltage we know the resistance because
we went to resistance on our multimeter and we actually tested the resistance here so we know
the resistance value so the only thing we don't have is i so this wouldn't be the right equation
to use it's just more difficult because you got to move everything around so you want to use this one
that leaves i by itself and you can use these two values so you would use i equals e over r we know
e is 120 oops 120 and we know our resistance is 10 ohms so zeros cancel out and we get 12
amps so what does that tell us about uh the proportionality it doesn't really because
we need to do another example to see by changing one of the values if anything changes so we know
that with 120 volts and a 10 amp resistor we have 12 amps of current running through
so what happens if we double our voltage and we go to 240 volts but we keep the resistance
the same just raising voltage to see what happens with current so we have 240 volts
we have a resistance of 10. zeros cancel out we get 24 amps so our amperage has increased because
our voltage has increased so those two values are directly proportional if you raise your
your voltage in one the current flowing through the circuit is always going to be more
if the resistance stays the same in both scenarios so let's change a different value say we want to
find our resistance and we don't know the resistance we can't get into whatever we're doing
to like actually measure any kind of resistance we're getting on it but we do have our ammeter
and we can clamp around it and see oh we'll add 100 at 240 volts that's running that's a you know
potential across this resistance it's drawing 5 amps so we know these two values but we don't know
resistance so we're going to use this one because we want to get the answer for that and we already
have those two values so if we have 240 volts and five amps of current running through it we would
just do 240 divided by five that is 48 ohms of resistance so in this situation 48 ohms okay so
let's try to change something again let's change our current to see what it does to the resistance
so in this situation still 240 volts but we're going to have 15 amps worth of current
on the circuit now so there's a lot more current flowing which means there's less opposition to
current so it should go down the resistance number should should decrease so we take 240 volts
and divide that by 15 16 ohms so now we know our resistance has gone down
but our current has gone up so current and resistance have an
inversely proportional relationship we found out that voltage and current
have a directly proportional relationship so what about voltage and resistance so voltage
and resistance if we look at an equation how an equation is laid out you can tell really easy on
the equation what values are going to be in which proportionality to each other i equals e over r
because we have a value that's a numerator here like basically i is the same thing as i over one
so this is always the numerator this is always the denominator anytime you have a numerator that has
a denominator on the other side these two values are always going to be inverse of each other
and any values that are on the top side the numerators are always going to have
a directly proportional relationship so we have these two different equations we have e equals
or i equals e over r so i and r because one is in the numerator and one is in the denominator
this and this are going to have an inverse relationship to each other they're not going to
be directly proportional same thing here and here we just flip the sides really really you know but
that's the only thing in all of these equations that is inversely proportional everything else is
in a numerator so it is all directly proportional so both if you take the current uh if you take you
know the current amperage and the voltage and you increase one you're going to increase the other
also if you take voltage and you take resistance and you crease one of them or the other it's going
to increase both of them so there's no denominator in any part of that equation so i hope that
answers your question current and resistance in an electrical circuit are always going to
be inversely proportional raise one one's gonna go down everything else is directly proportional
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