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DC electricity and Ohms Law

Picture 1: An electrical circuit

I have decided to teach several sessions on electrical theory.  This is the first of the several.  I thought long and hard about starting down this path because this site is about creating and making things.  Unfortunately, I know of no way of creating electrical things without knowing the theory behind it.  Both the audio file and text cover the same things, but the audio does have some additional (and probably useless) information.
Before going into the theory, I would like to describe where I want to take us.  At the start of this I will be talking about DC theory up to the point where we can actually start designing some simple amplifiers with an electronic circuit called an Op-amp.  Specifically, we will design a circuit that will allow us to measure temperatures using a thermistor.  Once we get a little further into the theory we will learn two energy storage devices, a capacitor and an inductor.  Those will give us the ground work to understand many physical properties by making analogies.  As a mater of fact we will be making an analogy today as we start the first step.

Electricity consists of charged particles.  If the particles are stationary we have static electricity.  This is the kind seen in some of the the fun science shows where someone puts their hand on a Van de Graff generator and their hair stands up.  The point of that experiment is that they are charged with one type of charge and since similar charges repel each other their hair stands up.  The kind of electricity we will be talking about is where charged particles are moving.  This happens because an electrical source provides excess charged particles at one terminal and a deficit of those particles at the other terminal and a circuit connects the two ends together.   When electricity was first being described, they said the terminal with the excess would be marked + and the terminal with the deficit would be marked -.  They guessed wrong!  It turns out that electricity flows from the negative end toward the positive, but by the time that was determined lots of scientific papers had been written and all the mathematics had been written assuming it went from + to -.  The direction from + to – is called “conventional” flow and the direction from – to + is called electron flow.  We will be using the conventional flow throughout, but you may run into information elsewhere that shows the opposite.  The electron flow is more correct, but it really doesn’t matter because we cannot actually see it.  The conventional flow is easier to use because for example, when we look at data-sheets of devices they may refer to a source or a sink and that will be the + and – respectively.   (It just is the way it is…. sometimes it is best to just “go with the flow”… pun intended.)

The way we will think of the voltage source is like a water tank sitting high on a platform.  Gravity creates a head pressure on the water and if it has a path to flow it will flow through pipes down to the ground and do some work.  Voltage is analogous to Pressure.  The term once used to describe the force driving the charges was electromotive force, but today most simply call it Voltage.  The flow of the electricity is measure in Amperes (most just say Amps) and is analogous to the flow of water in gallons per minute, or litres per minute.  As shown in the picture, I draw Voltages in a circuit as dimension lines and I show current flowing by drawing arrows showing it flowing.   The reason for this will become obvious very quickly.   Please note that in that drawing, I show the current flowing from the + terminal of the source to the load and that end of the load will become + also.   Next the current flows out of the – end of the load to the – terminal of the source.

Now you are probably saying.: “The analogy is no good, water does not have to flow back to the tank and make a circuit.”  You would be correct on the short term, but if the tank is going to continue to flow water current somehow it has to get refilled.  Somehow there has to be a pump to pump the water back up to the top of the tank.  This is true even if that pump is mother nature evaporating the water and causing it to fall as rain on a roof that fills the tank.  Water does make a circuit or loop.

Picture 2 the load has been replace by a resistor.

As the water flows out of the tank, friction in the pipes and possibly other restriction devices control that flow.   The load serves that function in electricity.  In the 2nd picture I have replaced the load with a device called a resistor.  The resistor is given a value to describe how much resistance it provides to the flow of electricity and this value is given in the unit Ohms.  This unit is often shown with the Greek symbol Omega, Ω.

The fundamental law of electricity is called Ohm’s law.  It states that the current  flowing in a circuit is equal to Volts divided by resistance.    This is written: I = V/R   where I = the current in Amperes, V = the Voltage. and R = the Resistance in Ohms.   Please note that you may find this written I = E/R  where E is the Electromotive force measured in Volts.   In the circuit of Picture 2.  The current = 10 Volts / 5 Ohms or 2 Amperes.

Since most people are concerned about how fast the battery will discharge or how much their power bill will be, we have kind of an interesting situation here.  The greater the flow, we would say the greater the load.  But this greater load would be due to less resistance.  This means “load” is the inverse of the resistance.   The same thing is true of the load on the water supply system.

Picture 3: Two resistors in series

So far our circuit has not been very interesting, but do not fear… I will start complicating things!   Let’s now say we connect two resistors in series.  Since the electricity must flow through both the total resistance of resistors in series is the sum of those resistances.    In this case our total resistance = 5 Ohms +5 Ohms or 10 Ohms.  Using Ohms law our current flowing out of the source would be 10 V / 10 Ω = 1A.

Now things start to get a little interesting.  Since the 1 A of current must flow through each 5 Ω resistor, each resistor has a 5 V  ( Ohms law transposed: V = I X R).  Now you can see why I choose to draw the Voltage in the circuit using dimension lines.  Each of those voltage drops add to produce a total voltage drop of 10 volts.  It is as if we divided the voltage in half in this case.  As a matter of fact, that is what this circuit is called, a voltage divider.



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