## Saturday, August 29, 2009

### DC Series Circuit Part 1

I just want clarify something before we start our new topic for today. I think you realized why I'm posting such very basic topic. This is not to insult your intelligence but the purpose of this is for you to comprehend well the basic first, because in reality some of you do not understand the basic. This is one of the common mistakes of the beginners especially taking up the course like Electrical Engineering. If you would ask me if I have a plan of posting an advanced concept. Simply the answer is YES , PERIOD. But this is after posting up all the basic concepts.

Please bear with me for a sort of introduction. Just want to clarify something.

Moving on...

Resistance in Series Circuit

Have you already read the definition of a series circuit in your Physics? Well, if you forgot it already I will define it for you again to refresh your mind. If you still remember our example of a light bulb connected across the battery source, that's already a typical example of a series circuit. But in this case, since we are dealing of resistive circuits, we will define it in this way.

A series circuit is formed when two or more resistors are connected from terminal to terminal or simply end-to-end in a circuit in such a way that there is only one path for current to flow.

Connecting the resistor in series so as to form series connection is much easier. You don't have to worry about connecting positive and negative terminal. Resistors (unlike cells) have no polarity.

I just want to clear this things up for you. If you have for example a two lamps connected together from one terminal to another leaving each other terminals of each lamps unconnected, this is a series connected but you would not have a so called series circuit. In order to have a series circuit, you would have to connect the lamps across the voltage terminals such as a battery for example using the unconnected terminals to complete a series circuit.

Remember, any number of resistance, lamps or any devices connected together in a series would only be a series circuit provided their end to end terminals are connected across to a voltage source and would offer one path of current flow. Ohhh... I just can't proceed with the discussion without showing you the typical example of a series circuit. A very good representation of a series circuit was given below.

One important thing that we need to remember here in series circuit is that their values are just added. The regular reader of this blog still remember the discussion about factors upon which the resistance of conductor depends. It was mentioned there that the resistance of conductor increases as the length of the conductor increases. In order for you to get my point here, imagine you have a 3 different length of wires in your hand with different resistances. Then, lets try to connect it together. After connecting them together, the resistance of the wire in full length would be equal to sum of resistances of wire 1 + wire 2 + wire 3.

Let's take it again into more detail... another example if I have a three lengths of wires. The first one having a resistance of 3 ohms, the second is 4 ohms and the third one is 5 ohms. If to try to connect them together, the total resistance of the end-to-end terminal would be 12 ohms. The conclusion here is that any types of resistances connected in series, their total resistance would be equal to the sum of their individual resistances.

One more thing that we need to consider when dealing with resistance connected in series is the proper identification. So, what is this all about? When dealing with a circuit, you would surely encounter different equivalent value of resistances just like what we have in our examples above. In order for you to distinguish same device with different resistances to another we have a so called subscript for them to identify.

This subscript was now written in a different manner. Today it was written like R1 ( not offset) which is similar to R1 ( which is offset) like the above diagram. R1, R2, R2 identifies same resistor with different or same resistances. The same manner was also applied to voltage E1, E2, E3 or sometimes they use V1, V2, V3 just like given in the above example diagram. For uniformity, lets use Rt with the small subscript t for the total resistance. For example on the above diagram our total resistance is Rt = R1 + R2 + R3.

Remember to use the correct subscript, because when we deal with more complicated circuits, you would not be confused. In any aspect aside from this, it is very important to distinguished one equivalent value to another.

The Flow of Current in Series Circuit

Since we already know that the current will flow in one path in a series circuit. This only means that the current will flow in every component of the circuit. Since I'm a visual person, I would give you a practical example of this. Supposed you have a circuit just like what we have on the above example, let's put an ammeter across a resistor one at a time to get the current reading. It would show that there are identical amount of current is flowing in every component in the circuit.

Take note that the current must be capable of passing in every component in the circuit without being damaged. What does this mean? Let's take gain another example. If you have a light bulb to be connected in circuit, it must be rated. If it is rated too low, the light of the bulb would be very bright and the tendency of this light bulb would be burn out because of excessive flow of current. The same thing would happen if in practical application, you mistakenly use different ratings would result sometimes to a serious trouble. The circuit would probably stop functioning or will not function properly. This is very very important.

Voltages in Series Circuit - The Kirchhoff's Second Law

We all know that the current are just identical in every component for a series circuit. Now, let's consider the voltage across each component in a series circuit. This is somewhat we called it a potential drop or the voltage drop. Since they have same current, the energy expended in pushing this equal amount of current through the individual component must be also the same.

Let's consider the diagram given above. Supposed you have three resistors connected in series. The diagram shows that you have 45 V connected across the circuit. If we measure the voltage across R1, the reading would be 10 V, getting the voltage across R1 and R2 would be 30 V and lastly getting the voltage across R1, R2 and R3 would be obviously 45V. This is similar when we get the voltage across each resistor and sum it up would be also equivalent to 45V. See the diagram how it is clearly illustrated.

The fact above was expressed by the German Physicist Kirchhoff (1824- 1887) which is known as Kirchhoff s Second Law. The first law would be discuss on my next succeeding post. Please take note of what this law being state and it is very important too.

Kirchhoff s Second Law states: The sum of the voltage drop across the resistances of a closed circuit equals the total voltage applied to the circuit.

Applying Ohm's Law in Series Circuit

Simplifying the facts that we have above about series circuit. We now know that:

1. The current in the series circuit is the same everywhere. This can be mathematically expressed as It = I1= I2= I3 and so on.

2. That the total resistance in a series circuit is equivalent to the sum of the individual resistances in the circuit. This can be expressed as Rt= R1 + R2 + R3 and so on.

3. That the voltage drop across each resistances when added is equal to the voltage source connected across the circuit in series. This can be expressed as, Et = E1 + E2 + E3, and so on.

Applying ohm's law in a series circuit is very helpful especially in terms of application. For instance, you do not know the value of the resistance connected across the circuit but you have some data to resolve that problem. Ohm's Law would be a great help for this.

Some useful application of Ohm's Law in the series circuit is the simplication process. Let's take an example diagram below.

You will in the example above that the right hand diagram is the simplified version of the left hand diagram. With this theory, you can find some missing factor that you want to know in your circuit. You should always try to simplify the series of resistances into single resistance equivalent circuit just like what had shown above. Let's simulate a good example of this.

A sample problem...

A circuit contains two resistors connected in series across 100 Volts. The circuit current flow is 2 Amperes. One of the resistor R1 have known value of 10 ohms. You wish to know the resistance of the entire circuit, the value of the second resistor R2 and the voltage drop across each of the two resistors.

First, in Ohm's Law Rule, lets draw the diagram just what had shown above. Since we already visualize on how we are going to simplify it, let's make a list of the given and unknown values.

Data:
Et = 100 Volts
It = 2 Amperes
Rt= (unknown)

E1= (unknown)
I1 = 2 Amperes since It = I1 = I2 = 2 Amperes
R1= 10 ohms

E2= (unknown)
I2 = 2 Amperes
R2 = (unknown)

Now let's solve it!

Since we are looking for the resistance of the entire circuit, from Ohm's Law we use the magic triangle. Put your thumb on R. Now we obtained that
Rt = Et/ It = 100 / 2 = 50 ohms - answerIf you will see, you cannot obtain the value of the second resistance R2 without knowing first the voltage drop across R1 which is E1. After knowing the value of E1, we can now proceed in solving the voltage drop across R2 which is E2 therefore we can solve for the unknown R2. Let's do it...

From the magic triangle, put your thumb on E, therefore voltage drop across R1 is E1 = I1 X R1 = 2 x 10 = 20 Volts -answer

From our concept above, the sum of the voltage drop across each resistances is equivalent to a voltage source connected across them. - Kirchhoff s Second Law

Et = E1 + E2 ; 100 Volts = 20 Volts + E2, solving for E2 = 100 - 20 = 80 Volts - answer (simple algebra dear)

Since we already know the value of voltage drop across the R2, we may now solve the value of R2. Putting your thumb on R of the magic triangle, we obtain that
R2 = E2 / I2 = 80 / 2 = 40 ohms - answerTry to practice more solving a series circuit using ohm's law. It is important that you should grasp the use of Ohm's Law in solving series circuit.

I will continue the discussion of DC Series Circuit here in Electrical Engineering course.

See you again.

Note : I'll be back on September 3, 2009 evening (Philippines Time) for continuation of DC Series Circuit Part 2.

Cheers!