Tutorial: Electrical impedance made easy - Part 1--- make money online

hey everyone I thought I'd talk a little

bit today about electrical impedance

this is a topic that confuses a lot of

people probably because it's taught sort

of backwards in my opinion where a lot

of people you know spend all their time

on the heavy-duty math involved and then

kind of end with a practical circuit but

I like to go the other way and start

with a practical circuit and then as we

move along uncover the topics as they

become relevant so let me show you what

I have set up today our task for today

is to build a circuit that can power

just a standard cheapo plain led

directly from the AC mains while using

as few components as possible and to do

it in a relatively energy efficient

manner so to start we may come up with a

circuit that looks something like this

where the LEDs are set up back-to-back

so that as the AC power switches

direction one of the LEDs will light up

so one will be on for both halves of the

cycle but obviously we can't connect the

LED right up to to house current because

the voltage is so high that there would

be way too much current flowing so if

you just took an LED don't do this by

the way and just put it right into the

outlet it would probably explode in a

violent pop because the amount of

current would be measured in you know

hundreds or thousands of amps or

something so we can do to keep that from

happening is to put a big fat resistor

between the LEDs and the the loop formed

by the power source so how do we figure

out what resistor value we can do that

by measuring the LED I measured this

cheapo green LED and it just came out to

be about 18 milliamps at two volts and I

got that number just by connecting it to

my power supply and just getting a

really quick you know rough reading okay

so if we know that the voltage across

the line is a hundred twenty volts on

average for one cycle

the current will flow out through the

line through the diode through the

resistor and back and this whole thing

reverses obviously when the AC goes into

the other phase so we'll just look at

this one phase so we've got 120 volts

here 118 volts here because we know the

diode is going to drop two volts at the

proper current and then the resistor has

to drop a hundred eighteen volts at the

proper current so then we just use Ohm's

law voltage over current 118 volts over

18 million member to always enter the

units in standard units so amps not

milliamps and we end up with 6.6 kilo

ohms okay easy enough now what I'm gonna

do is just change that up just a little

bit and this will become clear later on

what I'm gonna do is put 1k here and

five point six K here and that may seem

a little strange right now but this will

make sense later on the LEDs don't

really care whether the resistor is on

the left side or the right side

so splitting the resistance stuff like

that doesn't really change anything with

the circuit so here it is you can just

see the the small resistor the two LEDs

and this is a big resistor using a big

resistor is necessary because this is

going to dissipate some pretty serious

power I should also point out that

unless you're familiar with the hazards

involved with you know AC line current

you probably would not want to try this

one home this is more of a demonstration

so I'm gonna plug this in the LEDs come

on and hopefully you can see yeah its

drawing about 2.2 watts according to

this meter so 2.2 watts for those two

measly resistor or two measly LEDs it's

not very good at all if you were an

electrical engineer and you came up with

this the Energy Star people would not be

very happy with you at all so I'm gonna

unplug it and just after this just after

there's five five or 10 seconds of

running

this this resistor is you know not

burning hot but pretty good good and

warm and if this were left running for

10 minutes or something that resistor

might be too hot to even hold it said

well it's a 5 watt resistor it would get

pretty warm so we got to come up with

another design and that design is this

so what I've done is replace the

resistor this was the first design here

I want to say basically just replace r2

with a capacitor so you might be

thinking well what's that going to do

they actually serve a very similar

purpose in the circuit they both serve

to limit the current so let's I built

the capacitor circuit that's over here

basically the same thing with just a

capacitor in place of that fat resistor

let's plug this one in the LEDs are

about as bright as they were the first

time but notice the power meter it's

only drawing 0.4 watts instead of 2.2 so

our change the change from a resistor to

a capacitor has actually made our

circuit quite a bit more efficient so

let's take a look at why I'm gonna

unplug this and also discharge the

capacitor it had a little tiny pop I

don't know if you heard that or not but

you wouldn't want to if you did build

this circuit keep in mind that when you

unplug from the wall here that capacitor

is gonna store a charge and you know

just short it out like this like I say

you should probably be familiar with

with 120 volt safety if you're going to

attempt this one so let's take a look at

that schematic again okay so I said that

the capacitor and the resistor in the in

the first circuit are serving similar

purposes they're both restricting the

amount of current that can flow through

this circuit and this the units that we

use to describe a restriction of current

are ohms so these both actually have a

value that we can state in ohms but why

are capacitors not rated in ohms like if

you go to

the electronics catalog and look down

the list of capacitors nothing is in

there is gonna say anything about owns

so how do we do it we use this formula

right here one over two pi times the

frequency in Hertz times the capacitance

in farad's so this capacitor is 0.47

micro farad's and the frequency is 60

Hertz because we I'm in the United

States and all the line power is 60

Hertz here so 1 over 2 pi times 60 times

0.47 times 10 to the negative 6 and if

you calculate this all out you get 5.6

kilo ohms just like in the first circuit

they're almost exactly equivalent and so

this this value here X is called

reactance and reactance is basically a

resistance to alternating current flow

so they're both you know in ohms this is

the same own value as the resistor the

difference is that the reactance depends

on the frequency so the reason they

don't print capacitors with own values

in a catalog is because they don't know

what kind of circuit you're gonna put it

in so if we were using this in Europe

where the power is 50 Hertz the own

value would be slightly different

because the frequency is different

so what's impedance impedance is the

combination of reactance and resistance

unfortunately we can't just add them

together impedance which is represented

by Z is equal to the square root of the

resistance squared plus the reactance

squared and you geometry guys out there

will see that this is how to calculate

the length of a hypotenuse knowing the

leg lengths of a triangle so we'll get

into this later but just for now I just

wanted to show you where impedance comes

from impedance is just the combination

of the pure DC resistance and the AC

resistance known as reactants so the

impedance of a resistor Z equals the

square root of R squared plus Z

because the resistor doesn't have any

reactance a resistor has the same

resistance at all frequencies if it's

perfect a capacitor has no resistance if

it's perfect and it has reactance so the

impedance of a pure resistor is just the

resistance and the impedance of a

capacitor is just the reactance and we

had the formula here for the reactance

of the capacitor is just 1 over 2 pi the

frequency times the capacitance so I'm

just going to show you that you can if

we let's say we wanted to know the

entire amount of RP dance for our whole

circuit here what's what's the impedance

for this whole thing we're gonna make a

really nasty assumption here we're going

to assume that the LED is actually

behaves like a resistance which of

course it doesn't but in this case it's

not going to make much difference

because it's such a small part of the

circuit so here's the Z total for our

hole we're going to approximate the

resistor with a 110 ohm resistor so

we've got 1k plus 110 squared plus 5,600

squared and take the square root of that

so the entire impedance for the whole

circuit is 5.7 kilo ohms so basically

impedance is just a resistance that

depends on frequency that's really all

it is

and so with a capacitor at higher

frequencies it will have a lower

impedance and a higher impedance at

lower frequencies so I think what would

happen if you took a capacitor and just

put it across a power supply once the

capacitor charges up no current flows

because that capacitor is infinite

resistance at DC currents let me just

draw this out here for a capacitor this

is reactance and this is frequency when

the frequency is low it's you know zero

basically the reactance is infinite

at the high frequencies the reactance

becomes a very low value and this has a

a one over F relationship because of the

formula we had 1 over 2 pi FC so you can

see that for any capacitor at 0 it's the

Imperius and resulting impedance is

infinite and at infinitely high

frequencies the reactance is zero so for

infinitely high frequencies the

capacitor is like a short sometimes the

water analogy is helpful so think of

electrical current like water flowing

through a pipe in the case of a resistor

in our circuit here the electricity

flows through here and is restricted the

flow is restricted by these resistors

but in the case of the capacitor the you

know water or electricity flows into

here in the capacitor acts like a bucket

so the water flows into the bucket and

it fills up the bucket and once the

bucket is full

nothing nothing continues to flow the

circuit basically stops but in an AC

circuit the voltage flips and in our

case 60 times a second so when the

voltage flips polarity the bucket dumps

its contents back through the circuit

and makes these LEDs light up so you

might be wondering how does our circuit

become more energy efficient it has the

same impedance we said that we show that

these circuits are almost equivalent we

had five point six K for this resistor 5

point 6 K for this capacitor this is the

same this is the same how come the power

meter only read 2 point 2 watts for this

case and only point 4 watts for this

case we're going to talk about that next

time in the exciting conclusion to our

series on impedance here where we're

going to talk about power factor volt

amps and watts if you've ever wondered

about those things I'm going to talk

about those next you can actually use

these these cool little power meters to

measure power factor volt amps and such

ok I hope that was helpful

stay tuned and subscribe for future

electric electrical tutorial

and feel free to post comments about

what you'd what topics you'd like to see

okay see you next time bye

PostScript so you might be wondering why

I left this resistor in with the

capacitor circuit I said that we could

you know size a capacitor such that it

would replace almost any impedance that

we want in this circuit so why did I

bother leaving this resistor in it's

actually more of a practical matter I

mean if in a perfect world we definitely

could build this circuit without any

resistance and make it purely capacitive

use just a capacitor to limit the

current but here's the problem in in AC

current you know we have a cycle that

looks like this and at some point we

have to build our circuit and then plug

it into the wall so if we happen and and

this is just running constantly so if we

happened to plug in our circuit right at

this point in time everything would be

great the circuit would see a wave that

was nice and and and you know starting

at zero and flowing up and down normally

but what happens if we decided to plug

in our circuit here that wouldn't be so

good so then you know if zero is here

our circuit would see something like

this voltage would be zero and then

suddenly we put the plug into the outlet

and suddenly we get a nice sharp

transition right up like this and then a

nice smooth sine wave now this sharp

edge right here is not sixty Hertz it's

actually composed of a bunch of

frequencies many of which are higher

than sixty Hertz so our capacitor has a

much lower impedance during this very

sharp spike this very sharp voltage

transition and that would cause too much

current to flow through the circuit and

it would cause the LED to die so I tried

it you know obviously I wanted to find

out what would happen myself so I built

the circuit you know just like you see

here without the resistor and plugged it

in and after about ten

cycles of me plugging and unplugging it

the LED was just about toasted it would

still light but kind of dimly it wasn't

doing very well so during this really

short time this is probably only gonna

last about a millisecond there will be

much higher current flowing through the

LED so this limits the so called inrush

current and it's purely a practical

matter just because you know you can't

plug in your circuit at the zero cross

point every time you have to anticipate

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