Voltage
Current
Resistance

Ohm's Law

Types of Circuits
Series
Parallel
Series Parallel

Power

Voltage drop

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ELECTRICITY

Is an invisible force. The force is the attraction or opposition between charges. I am not going to get into the electron and proton in the atom but you should have some understanding of how electrons flow through a conductor. The main principal behind current flow or the flow of electrons through a wire is the potential difference between charges. As we are aware Magnets have north and south poles and if we bring the same poles together there is a force that is trying to repel them but on the same note if we use opposite sides of a magnet the will attract.  On a battery we have a positive and a negative terminal ( opposites) .  If we were to attach a wire to one end of the battery and bring it close to the other end of the battery,  as soon as we were close enough where the potential difference ( voltage ) was able to overcome the resistance of the air,  electrons would flow or attract and we would have a spark. Electrons with a path to travel will be attracted to the opposite terminal and repelled from the alike terminal.

 

Named after Alessandro Volta. Fundamentally,  the volt is a measure of the work needed to move an electrical charge. We can also use the terms pressure or force to explain voltage.  The symbol for the potential difference is V. Sometimes the symbol E is used for emf. (Electro motive force). 

Named after Andre M. Current is the movement of electrons through a conductor and is expressed as ampre A. The more flow of electrons the greater the current.

Resistance is the opposition to current flow . Every medium has some resistance and the resistance of an object is determined by the nature of the substance of which it is composed,  the dimensions of the object , and the temperature this is known as resistivity. Resistively is expressed in terms of the ohms resistance per cubic centimeter of the substance at 20° C (68° F). As we know light bulbs , motors, electric heating elements and relay coils all have resistances even though they are just wires. For this next section lets assume all wiring has no resistance.

 

 

Ohm's Law is one of the most useful formulas you will ever learn, It is the most basic law of current flow and is named after it's discoverer Georg Ohm. his law states that the amount of current flowing in a circuit made up of pure resistances is directly proportional to the electromotive force impressed on a circuit and is inversely proportional to the total resistance of the circuit. In English what he is saying is that the amount of current flowing through a circuit is directly proportional to the voltage being applied to the circuit and inversely proportional to the amount of resistance in the circuit.  What does all that mean,  if we increase the voltage in a given circuit and the resistance stays the same the current will increase, or if the voltage is the same and we increase the resistance the current will drop. 

 

 

E = Voltage also known as E in E= I x R

 I = Current also known as A or amps

R= Resistance also known as ohms

 

Ohms law can be applied to both AC and DC circuits but due to the complexity of AC and invoking inductances and capacitances I will speak directly about DC as this will give you the most basic understanding.

DC or direct current is current that flows in one direction. I would like you to think of it as water flowing through a hose .  Voltage will be the city water pressure and the resistance will be the spray nozzle at the end of the hose.  If the water pressure is a constant 60lbs and we hold the hose nozzle fully open so that there is little or no resistance to flow a large amount of water will flow through the hose . Now if everyone on the street turned  their water on and the city water pressure dropped to 30lbs the amount of water flowing through the hose would be far less, so before our water would shoot 20 feet out of the end of the hose,  now it only shoots 10 feet (current was reduced). If we go back to the 60lbs water pressure and only hold the nozzle open half way the result would be the same we would only spray 10 feet but yet our pressure is still 60lbs WHY ?  we increased the resistance to flow and therefore reduced the amount of water flowing . Now lets put that to a DC circuit.

Jim has an idea so he takes the 12 volt battery out of his boat and hooks it up to a control circuit. When everything is connected he puts his amp meter in the circuit and he gets a reading of 6 amps. How does Jim find out how much resistance the circuit has ?.

E = I x R

E = 12 volts, I = 6 amps & R = X

 or

12 = 6 x R

R = 12/6

R = 2 ohms

In this example if we were to double the voltage to 24 volts what would our resistance be ?

R = 4 ohms

Look at the figure above and answer the following.

1.  6V power supply and we add a light bulb with a resistance of 4 ohms what will our current be ?
2. 12V power supply and we measure a current reading of 8 amps what's our resistance ?
3. 24V power supply and a relay with a resistance of 6 ohms what's the current going to be ?
4. 36V power supply and a current draw of 10 A what the resistance.
5. No picture this time :)  we have a heater with a resistance of 8 ohms and the power requirements on the name plate say 120 V  what will the current draw be ?

Answers : 1- 1.5A  2- 1.5 ohms  3- 4 amps   4- 3.6 ohms  5- 15 amps

TYPES OF CIRCUITS

A series circuit is a circuit where there is only one path for current to flow,   just like in our water hose,  therefore current in a series circuit is always the same, any resistances in the circuit are joined from end to end and is calculated as follows.

R1 + R2 + R3 = R Total

In the fallowing diagram calculate the current .

R = R1 + R2 + R3

  R= 6

 V = 12

   I = ?

  Answer I = 2 A

In a parallel circuit the loads ar arranged to allow all the positive terminals to be joined to a single conductor and all the negative one to another conductor so in effect the current travels through different parallel paths. The total resistance of a parallel circuit is the reciprocal of the sum of the reciprocals of each resistor. Translated to English :) 

 

 

 

 

 

To calculate the total resistance in the above diagram will be as fallows

1/R total = R1 = 1/2   R2 = 1/4  R3 = 1/8        1/R total = 7/8    R total = 8/7 ( 1.143 ohms)

These circuits have both series and parallel branches in them , they are more complicated but we can easily work through them.

The best way to solve this problem is to break it apart into smaller ones. We have parallel branches here and each branch has 2 resistors in series with each other . To begin lets first combine the series resistors so all we will have left is 3 branches.

Path A = 3 + 4 = 7 ohms

Path B = 6 + 7= 13 ohms

Path C = 10 + 1 = 11 ohms

As you can see now all we have to worry about is the parallel part .

1/R total = 1/7 + 1/13 + 1/11 = 311 / 1001

R total = 311 /1001 ( 3.219 )

WHAT ?  if you've just shouted this out no problem we will work out the math. If you got this answer right just skip to the next section on Power by  Clicking here.

Our first parallel circuit was quite easy to solve with the numbers I used.

Our resistance were  2ohms,  4 ohms,  & 8 ohms if we divide these by 1 as the formula suggests we come up with .

1/2 + 1/4 + 1/8 = 7/8 we were able to work it out in our head because both 2,4 & 8 all divide evenly into 8.

or 1/2 = 4/8,  1/4 = 2/8,  1/8 = 1/8,  4/8 + 2/8 + 1/8 = 7/8  and when we divided 7 into 8 our answer was 1.14 ohms

This second problem seams far more confusing since how did we ever get 311/1001 ?

What we have to do is find a number that all the numbers we have divide into equally. Lets review our problem.

1. Path A = 3 + 4 = 7 ohms

          Path B = 6 + 7= 13 ohms

          Path C = 10 + 1 = 11 ohms

    2.   Apply the formula

        1/7 + 1/13 + 1/11 = 311 / 1001

1001 is a number that 7,  13,  & 11 all divide into equally. How did I get this number ?

7 x 13 x 11 = 1001   Ok that's easy but where does the 311 come from ?

Once you have the 1001 you divide the numbers into it.

7/1001 = 143,  13/1001 = 77 , 11 / 1001 =  91     143 + 77 + 91 = 311

311/1001 = 3.219 ohms

Lets now review the first problem.

1/2 + 1/4 + 1/8 = 7/8

2 x 4 x 8 = 64 

2/64 = 32 , 4/64 = 16,  8 /64 = 8 

32 + 16 + 8 =56

56/64  or 7/8 when broken down 

7/8 = 1.143 

 Congratulation's you've got it !

Power is the measure of the amount of energy produced or used by a circuit per unit of time. When current flows through a resistance, heat is produced.  This heat is the evidence that power is being used.  This is how a fuse opens, as the heat resulting from the excessive current,  melts the metal link and opens the fuse. Power is expressed in watts or VA.

Yes that's right that 40va transformer is 40 watts  VA = Volts x Amps.

Using this formula. assume you just picked up a 40 va 24 volt transformer and you want to fuse it what is the maximum fuse size you should use to protect the transformer ?

E = 24 volts 

I x E = 40 watts

24/40 = 1.66 amps

lets now look at a previous diagram.

1. What is the value of R 
2. How much power is being consumed by R

answer  1 .  E = I x R  6/12 = 2 ohms

answer 2 . P = I x E   12 / 6 = 72 watts

With current I through a resistance, by ohm's law the voltage across R is equal to  I x R .

What is the current in this diagram ?

I = 1 A,  4+6 = 10,  10/10 = 1 

Now Vt (Voltage total) = 10 Volts and this is being applied across Rt ( resistance total ) of 10 ohms therefore I is 1 amp.

Now that we know the current is flowing through the circuit We can calculate the voltage drop across each resistor buy applying ohm's law.

V1 = I x R1 ,   1amp x 4 ohms = 4V    Voltage drop of 4 volts from A to B 

V2 = I x R2 ,   1amp x 6 ohms = 6 V   Voltage drop of 6 volts from B to C 

Total voltage drop 10 V

 The IR voltage across each resistance is called voltage drop the total of all combined voltage drops will always match the exact supply voltage. 

Todd Legere

April 1 2000