Introduction to AC and Power: Power Series Part 3

Today I’m going to cover the basics of AC circuits, how they differ from DC circuits which I covered previously.  Again there’s going to be a bunch of math, please don’t get hung up on details.  If you’re confused by something roll forward and see if there’s something that helps clear it up.  If not, ask a question.  The math is merely a tool to help explain what’s going on, don’t get lost in it.

A side note from as I wrote this, I forgot how complicated a lot of this stuff is.  Seriously, most of the stuff on this page I don’t even give a second though and trying to remember how to explain it isn’t easy.  I have a heavy math background and it’s simple for me, though I know it won’t be for everyone.  I have no doubt someone’s going to get confused, seriously ask questions, please.

What is AC

The difference between AC and DC is how the current flows through the wire.  In a DC circuit voltage is constant and as a result the current will be constant as well.  AC on the other hand cycles back and forth at a particular frequency.  This cyclical action reacts with two of the three passive components previously discussed in a peculiar manner.  To make things simple we’ll start with a simple AC circuit.


An AC source is simply described mathematically as a sine wave.  Given the circuit as described we can find the current flowing through it at any time.


For those who can’t visualize what’s going on, here’s a graph.


Remember the relationship between voltage and current in a simple resistor circuit is linear so the current is always proportional to the voltage.  Now though we’re gong to talk about the two other components that react a bit differently.

Reactance and Impedance

Capacitors and inductors if you remember resist changes in voltage and current respectively.  We now are applying a voltage however that is constantly changing.  Now is where we discover a different type of resistance called Reactance.

Reactance is frequency dependent and describes how the component will react within the circuit.  It provides us with the information to find the phase relationship, as well define the current/voltage relationship at any point in time.  Reactance and resistance combine together to provide us an impedance.  This impedance helps provide a complete definition for the circuit.  First though we will discuss reactance from Capacitors and Inductors.

Reactance of Capacitors

Capacitors at low frequencies look like an open circuit since no current flows through them.  This is because at low frequencies the circuit almost looks most like DC.  While at high frequencies the capacitor appears to be a short circuit.  This is because a capacitor’s reactance is inversely proportional to the frequency.


Here’s a plot of reactance for a small capacitor, you can see it decreases as the frequency increases. For now ignore the sign, that will be discussed when Impedance is covered.

Reactance of Inductors

Inductors are the opposite of capacitors if your remember, and their reactance shows it.  At low frequencies the inductor appears to be a short circuit.  This is because the current isn’t really changing that fast so the magnetic field is quite stable.  This means that at high frequencies though the inductor appears to be an open circuit.  So while a capacitor is inversely proportional, an inductor is just proportional to the frequency.


Here’s the same plot as above but for an inductor.



The reason you didn’t need to worry about the sign is it doesn’t really matter until you want to know what has happened to the current.  Both of these items cause current to shift in time by an offset or “angle”. 

Finding the overall Impedance is actually quite simple, the why of this is a bit more complicated and is an entire post in itself.  The simplest statement is it is a result of effect the component has on the current voltage relationship.  To start with though impedance is found through the following equation.


This relationship allows us to find the phase relationship between current and voltage based off the reactance.  This is where that sign difference between the inductor and capacitor comes into play.  The (-) on the capacitive reactance equation means that the current will “lag” the voltage by 90 degrees if there is no other resistance within the circuit.  The imaginary values provide us a second axis to explain the relationship.

Remember one cycle is 360 degrees or 2π, so if we shift the current it can be measured from the relative 0. This leads us to phasor representation.  We can display the two axes together with just an angle and a magnitude.  I’m not going to go through all the details for phasors or what all can be done with them.

Here is an example AC circuit with only a capacitor:


The reactance and impedance can be found by doing the following:



Here’s a plot of a similar circuit with an inductor for comparison.


Why You Care

Impedance is a very important concept since it is required to help describe what is happening within a system.  This lead and lag concept and why it is important will become more obvious as we begin to start discussing power.

Power Basics

Power is simply the rate at which you are doing work.  In classical physics it is force times velocity.  Within the circuit however we can find the power being used by a component or being delivered to the system quite easily.   The power equation is defined as follows:


Given this we can also perform a substitution using Ohm’s law and find that the following also describes the power consumed by an element:


Previously it was shown how long wires can have very large resistances and that the voltage is stepped up for moving power long distances.  The above is why.  Since power is directly related to the voltage and current, it is much more efficient to have a much lower power loss caused by the wire.  Moving forward though we have the following graph of a simple AC circuit with current, voltage, and now a third line, power.


Notice how the power is pulsing.  This pulsing action is problematic for applications where you need a smooth and constant application of power.  This also creates a problem on the generator that can be quickly discussed.  Power can also be defined as the following:


A product of torque and angular velocity.  Now imagine that you’re turning a crank trying to lift a bucket from the bottom of a well.  If as you were cranking up the bucket at the top and bottom of the crank absolutely no force was required, not only that but the bucket didn’t move while there.  When pulling mid crank however the bucket moved quite quickly but it also required more force from you to pull.  All the while the rotational speed of you spinning the crank remained the same.  It would be very difficult, and from a mechanical standpoint it can cause vibration through the system.

To solve this issue we generate and distribute in what’s called three phase power.  Instead of supplying a single voltage and current we supply three, 120 degrees apart.  The total power being generated/delivered is the sum of all three.

Using that same sample circuit modified into a three phase system we get the following graph.


Notice the total power is dead flat, the three phase generator is always putting out the same amount of power.  The reasoning behind why this works will be discussed in the next article that talks about synchronous generation. 

What About Real Loads

So far my examples in the power section have only involved purely resistive loads where there is no impedance from capacitors or inductors.  In the real world though every type of load also provides some impedance that alters the phase relationship between current and voltage.

There are actually two types of power in the electrical system.  There first is real power, and is described as power actually consumed by the load.  The second is reactive power, this is power that is not consumed by the load but ends up in purgatory between the load and source.  These two are sometimes combined to create apparent power, which describes what appears to be supplied to the load according to the generator.

Mathematically it is described as follows:


The phase relationship between current and voltage leads to something called Power Factor or P.F.  It simply describes the weight between real and reactive power.  PF is found by the following:


Ideally you want a PF of 1 meaning the system is entirely in phase.  The reason for this is that a utility can only bill for Real power, they cannot charge you for reactive or apparent power.  Many companies with highly capacitive or inductive loads try to work this to their advantage.  The result is that the utility then bills them considerably more for the power they are using.  It is stressful to the system and is basically trying to cheat it.  The problem is easily solved by adding capacitor or inductor banks to even out the impedance of the load.

Let’s look at what happens to our power if we let our PF slip to say 30 degrees and why it’s such a problem.  This is the same exact 3 phase system shown above but the currents have been shifted by 30 degrees.


Notice the power delivered has decreased, this is because the current and voltages are no longer reaching their peaks simultaneously.  Instead the power delivered is equivalent to the original power multiplied by the power factor.


So there was a quick run down on impedance, calculating power, why we have 3 phase power, and what happens when we combine it all together.  Next week I’m going to talk about synchronous machines, how they work, and the basics of generation involving them. 

Its not sexual assault when they do it, but…

It is sexual assault when we do it

Mihamae now faces a felony count of sexual abuse.

What makes them so special?  They manage to get away with assaulting minors, yet we can not give them a taste of their own medicine?  The TSA is just a bunch of sick, diluted bullies hiding behind the government.  The abuse they dish out needs to stop now!  I applaud the woman who fought back.

Some feel that standing up and calling the people out as what they are is a fruitless endeavor as they are the “low man” on the totem pole. The husband and I feel differently because these individuals do have the ability to refuse to behave in this way. They can do their job while refusing to victimize and assault people. Their behavior reflects on them and who they are. If those who do behave themselves get caught in the crossfire so be it, they are responsible for restraining their compatriots. If they don’t like getting caught in the crossfire they can go find another job.

Obama and Reality, Never Shall They Meet

Obama placed on full display today how out of touch with reality he is:

President Obama on Friday kept up the pressure on Republicans to agree to revenue increases in a deal to raise the debt ceiling, claiming 80 percent of the public supports Democrats’ demand for tax increases.

“The American people are sold,” Obama said. “The problem is members of Congress are dug in ideologically.”

This is what we call reaching deep up into an orifice and pulling out a chocolate covered pretzel and calling it a gold nugget. A much lower claim around 40%, even 50% might be believeable. This just smacks of elitism and a superiority complex. Especially given the following:

As the Beltway politicians try to figure out how they will raise the debt ceiling and for how long, most voters oppose including tax hikes in the deal.

Just 34% think a tax hike should be included in any legislation to raise the debt ceiling. A new Rasmussen Reports national telephone survey finds that 55% disagree and say it should not.

Even if you dismiss the above, even within his own party he did not reach the 80% support he is claiming. America is reaching the end of her credit limit, the problem we have is those who are spending all the money can also arbitrarily increase the limit. Those at the head of all of this are totally out of touch with the public and are spending like drunken sailors on liberty.

Obama, as in touch with reality as a vegan running a steak house.

It’s amazing the number of people who still blindly support his actions and then proceed to claim the rest of us as racists. I am beginning to think no one really has the ability to think critically about things anymore.

Quote of the Day – Caleb(07/15/2011)

And then I realized something that I’ve always sort of believe but hadn’t really hit home until this morning: the traditional media is dead. Sure, they’ll shamble on like some horrid zombie repeating the same old tired lines and phrases, and of course 2012 we’ll see them full on in the tank again for Obama, but when it comes to breaking the news and doing proper investigative reporting? Yeah, you’re not really seeing that from the traditional media.

CalebPretend I said Something Smart

[No pretending required. That is a very accurate and well put statement regarding “traditional” media. I know Alan has touched on it from time to time, but traditional media is dead. There is nothing fair and balanced about the current news sources and it is a bunch of bloggers who are digging up dirt. Every blogger has something of their own they care about and has other stuff in the wings they watch. The benefit it the primary stuff is what brings everyone together and news from each our own little wings can take off like wild fire. We’re playing our strengths off each other and doing it quite well.

Weer’d the other day pointed how each of us adds onto the previous like one big circle jerk. The thing is that’s what makes us so damn powerful. We all approach it differently and connect dots that the rest of us haven’t seen.

Caleb, we don’t have to pretend you said something smart, you nailed it on the head. It’s bloggers who are breaking investigative news, not the mainstream media. When we break the news, it’s that much more powerful since each of us have different resources to bring to the table. We’re fast, we’re relentless, and there’s a very simple reason for that. We do this for ourselves. We have no vested interests other than those we care about. No one is paying us off, some of us make money, but even then it’s usually only enough to buy lunch in a blue moon. I fund this out of my own pocket and I think I’ve only made about $1.50 from the one google ad I have up. I don’t care though because that’s not why I do this and I know that’s not the reason most of us do this. -B]

Friday Gun Porn–07/15/2011

The Microsoft Object Embedding Tool.


Seriously, I’m not kidding!


Thug Recruiting on Craigslist

Airport “Security” is now feeling the need to hit up Craigslist for new recruits to A Security Theater


Customs and Border Protection

Immigration and Customs

You are need in our Airport! You are a vital person to help keep we the public safe, from terrorist attacks,keeping weapon off the planes.

Your our law enforcer! You work with personnel, people, and US Secret Service, If you have experience in working to protect the law and keeping the public safe.

We also need help in Customs and Border Protection, Immigration and Customs.

We need your help Prevent terrorist attacks, reduce vulnerability to terrorism, and minimize damage from potential attacks and natural disasters.

We have great pay, sign on bonuses and we have training for the right personal. If this sound like you a job that you

can do… then Hands Down and apply!

Honestly, Pullman Airport was the last hold out that my hubby thought maybe he could use to fly.  Not any more, since I have seen TSA agents in our small town and now the Craigslist ad.

Quote of the Day–Samuel Adams (07/13/2011)

If ye love wealth better than liberty,
the tranquility of servitude
better than the animating contest of freedom,
go home from us in peace.
We ask not your counsels or your arms.
Crouch down and lick the hands which feed you.
May your chains set lightly upon you,
and may posterity forget that you were our countrymen.

-Samuel Adams, August 1, 1776: Philadelphia State House

[I was reminded of this quote while writing a response to Ubu bad mouthing my suggestion to start turning up the heat on TSA employees over at Joe’s place.  Joe has obviously spent some time in contemplation of the subject.

I modified her closing remark into the following, striking out her original words:

I can’t think of anything more useless than a plot to verbally disrespect people to condone sexual assault, molestation, and humiliation of the law abiding under the guise of "security" and think it is going to accomplish something actually make us safer.

Ubu’s main contention is that it will not alter the behavior of those who work there and that it’s just a job to them.  The thing is if it’s just a job, then it’s just a paycheck.  The majority of your time is spent outside of work, if you can identify and harass these people outside of their normal employment the pay they receive for just doing their job will no longer be enough.  As for those who will do the job because they enjoy it, maybe those are parties that would be better served by some of the alternative methods Joe brings up.

There are numerous other ways to deal with the TSA and bring about their end, however for the most part we are confined by operating within the law.  Joe has valid points on the matter, but for all intents and purposes we all wish to operate within it’s bounds.  This also helps aid our case publicly since breaking the law can be manipulated into a negative detractor.  However our enemy in this case though has received a free pass and is even encouraged to violate and humiliate us despite what the law says.  Public humiliation is a well known motivator, especially when the pressure is applied in the correct manner.  There doesn’t have to actually be violence or threats for people to become uncomfortable enough to want to leave.

Ultimately the TSA is a joke and nothing more than A Security Theater.  Their record still sits at naught, while the people they have abused have actually done the work to protect themselves against the “terrorists”.  To understand what’s really going on, just think why I put quote’s around the word terrorist.  It’s because they have redefined that word to manipulate people into compliance.  What better way to completely invalidate your enemy than to make him a “terrorist” that the people will hate and despise, because who likes terrorists?  I’ve accepted that some may label me a terrorist, even though what they have done is twist the definition of a real patriot to that of the new “terrorist”.

So those who would rather lick the heels of the boots of our masters, go home, and may your chains set lightly upon you, and may posterity forget that you were our countrymen.  Patriots stand and call out tyrants and work to find a way to sop tyrants and their thugs instead of berating their countrymen and saying they look like assholes for it. –B

p.s. assuming this post works it means I fixed the problem. Fingers crossed.]

Today’s Power Series Issue Delayed to Saturday

For some reason WLW and my blog are not cooperating at the moment.  The previous post was actually hand written, I know who want’s to hand write HTML anymore.  So I’m going to spend today straightening it out, and then get back to writing up part 3 which will be an intro to AC and the basics of power.