Applications for DC Parallel Circuits

It's been a month and a half ago when I did an update on this blog. I've been busy with some things which I cannot explained to you right now. The reason why is that this project which is initiated by me is really intended for 2010. Although I'm doing a little update on this blog about Learning Electrical Engineering, the project still alive until such time I completed the course outline of this site.

I checked my stats awhile ago and I was surprised that my traffic still in tact with an average of 45 and above visitors a day. The number of subscribers is still increasing a bit compared when I started this blog. One thing you can expect from me, though I'm doing a little update on this blog, this site will still remain in search engines. I have now a PR2 from PR0. I would like to give thanks for those who supported and still visiting this site. Target keyword " learning electrical engineering " now dominates my rank in Google and Yahoo. Now let's continue of what I have left before.

The following illustrative problems below are just an applications of what I had presented on my post about DC Parallel Circuits.

• DC Parallel Circuits 1
• DC Parallel Circuits 2

From the previous post, I had illustrated to you the theory of the DC Parallel Circuits which consists of Part 1 and 2. Today, I will show you the application through problem solving.

Problem No. 1 : Let's begin solving parallel circuits in which I will show you how the current divides in each branch of circuits and how can we obtained the unknown values using Kirchhoff's Law. Suppose I have the circuit as shown in the diagram below. We need to find the unknown currents. We need to find the currents at I1, I4 , I6 and I7 . Click the image to enlarge.

Obviously, we can find the current at junction A by simply performing the KCL or the Kirchoff's Current Law. We can see that the current divides at junction A. Therefore, I1 = I2 + I3 = 7A + 3 A= 10 amperes.

Taking a look at junction C. We can see that the current entering this junction I2 divides into I4 and I5 which becomes a total current to I2. Therefore we can say, I2 = I4 + I5, which becomes 7 A = I4 + 5 A, and since we are looking for I4 = 2 Amperes.

Now, we would like to solve for I6. Since, the flow of currents I3 and I4 are flowing toward junction B. We can say that, I6 = I3 + I4 = 3 A + 2 A = 5 Amperes.

The last requirement is I7. Since the currents I5 and I6 are flowing toward junction D. we can say that I7 = I5 + I6 = 5 A + 5A = 10 Amperes.

The example above I had shown you is how the currents divides in each branch. The next example will illustrate you the application of unequal resistors in parallel.

Problem No.2 : Three loads A, B and C are connected in parallel to a 230 volt source. Load A takes 9.2 KW, load B takes a current of 60 amperes and load C is a resistance of 4.6 ohms. Calculate (a) the resistance of loads A and B, (b) the total resistance of the three paralleled loads, (c) the total current, (d) the total power. Click the image to enlarge.

Since we have different parameters given for each load, We have to solve first some missing requirements that we need in our calculations.

(a) Calculating Ra = Vt ^2 / Pa = 230 ^ 2 / 9,200 = 5.75 ohms

for Rb = Vt / Ib = 230 / 60 = 3.83 ohms

Note : The solutions shown above are just an applications of ohms law that we previously discussed.

(b) Calculating the total equivalent resistance of the circuits will follow:

Req = 1/ 1/5.75 + 1/3.83 + 1/4.6 = 1/ 0.174+ 0.261+0.217 = 1.53 ohms

Note : the formula used was just discussed on the previous post above DC PARALLEL CIRCUITS.

(c) Since we have already calculated the missing values, we can now solve for total current.

It = 230 / 1.53 = 150 Amperes

(d) To get the total power, since we already know the values of Vt and It. It will be now,

Pt = 230 x 150 = 34,500 watts or 34.5 KW.

For the above illustrative problem ( No.2 ) , I had shown you how the Ohms Law was also applied in solving the unknown quantities. This will surely applied when one value is missing. This is the best and basic technique that you can applied anytime you encountered such problems like this. The mentioned technique will also be applied when we reached complex AC circuitry.

This is the end of our basic circuitry in parallel connections. The next post will deal about series-parallel circuits lecture.

See you again on my next post.

Cheers!

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DC Parallel Circuits Part 2

Yes, let's continue of what we had left last time here in Electrical Engineering for Beginners. I was glad that you are still there and an increasing number of subscribers makes me feel more energetic in writing more in this Electrical Engineering course. But before you rolled your eyes over me, the coverage of this lesson for today is all about the unequal resistors, kirchoff's law and applying ohm's law in parallel circuits.

Last time, I had mentioned about solving the total resistance in parallel with equal resistors. I will tell you how it was derived when I reached the topic of solving unequal resistors in parallel within today. Let's begin to have a short introduction of unequal resistors in parallel then, I will insert Kirchhoff's first law before continue discussing unequal resistors in parallel. I did it that way because Kirchhoff's first law has something to do with the flow of current.

Moving on...

If the circuit contains resistors in parallel whose values are not equal or unequal, we have some difficulty in assessing the total resistance of the circuits. One easy way to get the total resistance in parallel is by using your ohmmeter to measure the total resistance. Suppose you have an R1 and R2 connected in parallel with 40 and 80 ohms respectively, you would obviously measure a total resistance of 27 ohms for that circuit.

Wondering how it was obtained?

In our previous lesson, DC Parallel Circuits Part 1. I had mentioned there that the current flowing in each branch of the parallel circuits are not equal if the resistances were also different from each other. More current will flow on the smaller resistance compared to that with bigger resistance value. All of them were mentioned in this post without some problem illustrations. I just only show you how the current divides parallel connections with varying values of resistances.

Since, it is not often possible to get the total resistance of the circuit by using an ohmmeter especially in this case our circuit connection is getting more complex, we ought to know how to get such values by using calculations. Previously, we had learned the useful concepts of Ohm's law by solving circuit values in series circuit connection. But in this case, there is another equation which you will need this time. It is what we have been waiting for. It was known as Kirchhoff's First Law - Second Law was already discussed here.

What was it all about?

Kirchhoff's Law is true in every type of circuit. The concerns of this law is not the circuit as the whole but only individual junctions where currents combine within the circuit itself. It's law states that : The sum of the currents flowing toward a junction always equal the sum of all currents flowing away from that junction.

Or, other states like this...

The algebraic sum of the currents at any junction of an electrc circuit is zero. This statement has something to do with the algebraic signs of the currents coming and moving away of the node. In order for you to understand this principle, take a look on the illustration below:

The image above is the simple representation of a circuit junctions. Suppose you have a four junctions there and all that conductors are carrying a current in the direction shown above. If you look at the image above IA are delivering stream of electrons at its node. It is obviously, that when the currents leaves that node, the current divides into IB, IC and ID which is equivalent to IA. Thus, making it IA = IB+IC+ID.

or, in other ways of expressing it...

IA- IB - IC -ID = 0, which also states on the above Kirchhoff's first law. In this case, it is important to know the direction of current. The current coming to the node is (+) positive while the current leaving, we'll assign a (-) negative sign for it.

I will be giving a pure problem illustrations of this topic on my next post this coming first week of October 2009 for you to comprehend well this topic. I reduced the frequency of posting due to my busy schedule at work.

Uhmm....

Unequal Resistors in Parallel Circuits

Here are some of the important rules to remember when dealing with unequal resistors in parallel:

1. The same voltage is impressed across all resistors.

2. The individual-resistor currents are inversely proportional to their respective magnitudes. You will understand this fully when I give you the sample problem on my next post.

3. The total current for the circuit is : It = I1 + I2 + I3+...

4. The total equivalent resistance of the circuit is:

Req = 1/ (1/R1) + (1/R2) + (1/R3) + ....

Note : When two unequal resistors are connected in parallel their equivalent resistance is equal to their product divided by their sum.

R xy = Rx x Ry / Rx + Ry

Ohms Law in Parallel Circuits

Just like series circuits, we were also need to apply Ohms Law when dealing with the parallel circuits. We will be using this law to calculate some other unknown quantities like current, voltage, and resistance in such circuits. This law would require less time and effort if you would have to know such quantities mentioned above.

Let's say you have a number of resistors connected in parallel but you like to measure the resistance of a particular resistor using your ohmmeter. Of course, you would first disconnect the resistor to be measured from the circuit otherwise, you will measure or the ohmmeter reads the total resistance of the circuits.

Another one, if you would like to know the current across the particular resistor of a combination of parallel resistors using an ammeter. Again, this time you would have to disconnect it and insert an ammeter to read only the current flow through that particular resistor.

Knowing the voltage requires no disconnection. But of course, Ohms Law is the very pratical use in knowing such quantities for electrical engineers like us.

These are just a short concepts for our Part 2 of DC Parallel Circuits. On my next post it would be a little bit lengthy for I will illustrate to solve problems related to this topic.

I will come back on first week of October 2009.

Cheers!

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DC Parallel Circuits Part 1

Before I proceed with my new post here on Learn Electrical Engineering for Beginners, I would like to thank those who sent their email for some questions. Keep those emails coming in. If you don't received an email from me that means the answer is already here on my blog or I will answer you on my future post. Please read below portion of this site for your guidance.

I hope you are now learning with this site. We are now moving on with our topic and let's study the next part of Electric Circuits which is DC Parallel Circuits.

One objective of this lesson is for you to understand that you can solve any circuits because all circuits are made of combinations of series and /or parallel circuits.

Previously, in DC Series Circuits we defined that whether resistors, lamps or cells are connected end-to-end. Today, the scenario would be completely different. Instead of being connected end-to end as in series circuit, they are connected side by side therefore it would create more than one path in which the current can flow. If this is so, we can say that resistors/resistances are said to be parallel connected or connected in parallel. The circuit would now be called a parallel circuit. The image below is one example of the parallel circuit. I show you this illustration because the diagram already explains everything.

As what I mentioned in our earlier topic about electric circuits, we cannot say a complete circuit if we do not have a source of emf connected to them. For instance, we have two resistors connected their wire in parallel or parallel connected. When any two terminals are connected across the voltage source just as what had shown above, the whole arrangement- both resistors, the wires connecting them together and the voltage source - forms complete parallel circuit.
The circuit above shows that there are more than one path of current to flow. This means that these two resistors shares on the total current drawn from the battery. A part of the total current goes through the first resistor and at the same time a part of the total current also drawn for the second resistor. If you will intend to connect a device with polarity, for example a cell or batteries, you must connect the positive terminals together and the negative terminals together.

The Voltage in Parallel Circuit

When the resistances are connected in parallel just like the diagram above and connected across the voltage source, the voltage across each resistors are always the same. Observe the diagram that the labels used were just the same. It was self-explained in the diagram that the voltage are just the same.

Since, it is the fact that voltages across each resistances are just always the same. It has a practical consequence. What do I mean with this? This means that all components which are to be connected in parallel must have the same voltage rating if they are to work properly. Did you noticed that?

The line voltage throughout the Philippines is 220 volts. In U.S. 120 volts. I think you are aware that some of our appliances are rated 120 volts or 220 volts work properly well. If in case you have a lamp or a bulb rated 20 volts. What the hell do you think will happen? The bulb will be burn immediately because the excess current will flow through it.

Since, all appliances are connected across the same voltage source, the same voltage will also experienced across each load. Each load must be properly rated to handle this voltage.

How the Current Flow in Parallel Circuits
In order to understand well the flow of current in the circuit for parallel connections. I made a little details on the diagram above. Take a look on the diagram below:

As I mentioned earlier, the flow of current in the parallel connections divides through each of the parallel paths. In the circuit diagram above, the two branches named them AB and CD connected in parallel. Observe that as the current flowing in each branches will divide and reunite them at node B returning to voltage source. You will wonder how the amount of current divides in each branches.

The amount of current that will serve in each branches will depend on the resistance value. This will be the principle: The current flowing through the several branches of a parallel circuit divides in inverse proportions, governed by the comparative resistance of the individual branches.
And so? what does this mean?

It only means that the lower resistance value in any branch circuit in proportion to the resistance of other branches in the same parallel circuit, the higher will be the current value or proportion which that branch will take.

Simply...

In parallel circuit, branches having low resistance draw more current than other branches having high resistance.

Like voltage, the flow of current connected in parallel circuit is also of a great importance. For instance, like we know that every electrical appliances connected in parallel, the current will divide unequally to each branch since they have differing value of resistances- the highest current flowing through the lowest resistance. You will learn more about this when we reached the protection against excessive flow of current.

Ohhh... I love to illustrate example again through problem solving. Let's take a sample problem for you to show that it really happens. Let's take again the circuit above and assign values for them.

Given that, I = 9 amperes ; I1 = 3 amperes ; I2 = 6 amperes

For instance, a total current I = 9 amperes is flowing through the parallel branch of R1 and R2. If you will observe, the value of R1 is twice the value of R2. We have mentioned earlier that the current divides in inverse proportion to the values of the two resistors. Therefore, only 3 amperes will flow on R1 and 6 amperes will flow on R2. If for example, R1 triple its resistance from 40 ohms to 120 ohms. The current flowing through R1 will be reduced from 3 amperes to 3/3 ampere or 1 ampere while I2 would remain unchanged. Thus the total current would be 6 amperes + 1 ampere = 7 amperes.

What does it implies?

Since, in series circuit we said that all currents are the same throughout the circuit. In parallel circuit we just add it. This can be expressed mathematically as, It = I1 + I2 + I3 +...

What if the resistances are equal in parallel circuit? This will be the next topic.

Equal Resistors in Parallel Circuits

Let's consider a water pipes connected in parallel as shown in the diagram below.

Let's say we have a constant water pressure incoming or the head as we learned in fluid dynamics. Assuming the same cross-sectional area of water pipes connected in parallel. The amount of water here would flow is equivalent to cross sectional area of pipe 1 + pipe 2.What do you think would happened to the amount of water flowing in the system if you would convert it to single pipe only? The amount of water will be less than that connected in parallel. Why? because you reduced cross sectional area in which the water would flow. The bigger the cross sectional area, the more water would flow on the system shown above.

The same thing in resistor. The bigger the cross sectional of resistor, the more current would flow because the resistor value diminishes as the cross sectional area is getting bigger.

The conclusion here is that : resistors or loads connected in parallel present a lower combined resistance or load than does any one of them individually.
This means that if you have four 400 ohms resistors connected in parallel. The resistance of the combined load will be equally divided into 4 equal resistances thereby giving you a 100 ohms total resistance. In other words, 100 ohms is your combined resistances of four 400 ohms connected in parallel.

If you don't get my point here, let's discuss it when we illustrate more problem solving in DC Parallel Circuits.

To be continued.....

Cheers!

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Applications: A Few Tips in Solving DC Series Circuit Problems

Before we proceed with to the Parallel Circuits, let's study first some other worded problems that you may be encountered during your board exam using the concept of DC Series Circuit. Learn Electrical Engineering for Beginners will provide you a technique on how you will overcome those scenarios.

The first problem that you will encounter is somewhat an application of a simple transmission lines. I just want to open this topic earlier because we will be dealing with this topic on my future post. I will just show you the snapshot on how those concepts that we studied in my previous post are being applied.

Let's begin...

Problem 1: The problem states that a load resistor of 4.1 ohms, 425 ft from 240-volt generator, is to be supplied with power through a pair of standard-size copper wires. If the voltage drop in the wires is not to exceed 5 percent of the generator emf, calculate (a) the proper AWG wire that must be used, (b) the power loss in the transmission line, (c) the transmission efficiency.

This is how you will going to solve it...

Let's have a simple visual of what is being said on the above problem. It could be shown just like the simple representation of transmission line below:

This simple transmission line can be considered as a circuit consisting of a 4.1 ohms resistor in series with 850 ft length of copper wire connected to a 240 volt generator. You would wonder why I say 850 ft length of wire while in the problem states that it is 425 ft from 240 volt generator. This is because in the given problem, it only mentioned the distance of the load resistor from the generator emf. It is not pertaining to the length of wire. Since, the load resistor has 2 ends connected to the wire across the generator emf, the actual length of wire should be 2 x 425 ft = 850 ft length. Please take note on this because there are many beginners who are getting mistakes when solving this type of problem.

Moving on...

The voltage drop would not exceed 5 % of the generator emf therefore,
Line Voltage Drop = 240 x 0.05 = 12 volts

Remember that in Ohm's Law in Series Circuit, the sum of all voltages across each resistances in series circuit is equivalent to the source emf therefore,
Load Voltage = Generator Emf - Line Voltage Drop = 240 - 12 = 228 volts

You have to consider the line voltage drop when dealing with transmission line.

The Line Current across the 4.1 ohm load resistor would be,
Line Current = 228 / 4.1 = 55.6 amperes

and the Line Resistance would also be,
Line Resistance, Rl = 12 / 55.6 = 0.216 ohms

We are about to find the resistance per 1000 ft. Using the ratio and proportion to get the resistance per 1000 ft. It would be,

Resistance (1000 ft)/ 1000 ft = Line Resistance / length of transmission wire
Resistance per (1000 ft) = (1,000 ft /850 ft) x 0.216 ohm = 0.254 ohm

a.) Consulting the AWG table below it shows that the standard wire size is No. 4; this wire has a resistance of 0.253 ohm per 1, 000 ft. This is based on the table below. Click the image to enlarge.

b.) Getting the actual line resistance would be,
Actual Line Resistance / 850 ft = 0.253 ohm / 1000 ft
Actual Line Resistance = 0.85 x 0.253 = 0.21505 ohm

We need to get the following data in order to get line power loss.
Total Series-Circuit Resistance = 4.1 + 0.21505= 4.31505 ohms
Total Current I = 240 / 4.31505 = 55.6193 amperes
Line Loss Power = (55.6193)^2 x 0.21505 = 665 watts - answer

c.) Getting the efficiency of transmission line can be derived in terms of load power and total power. This can be expressed as:

Efficiency = Load Power / Total Power = [(55.6193)^2 x 4.1 / 240 x 55.6193 ] x 100 %
Efficiency = 95% - answer

This is not not formal discussion about transmission line. We will touch it more in depth on my succeeding post. I'm just showing you how the concepts are being applied with these kind of application.

You would also encountered some tricky problems like what I will going to show you. This is just a simple one but you would used a simple ohm's law solving for unknown values. Let's have this example below:

Problem 2: A dc generator may be characterized by an ideal voltage source in series with a resistor. At the terminals of the generator, voltage and current measurements for two different operating conditions are Vt = 115 V at I = 10 A and Vt = 105 V at I = 15 A. Model the generator by a voltage source in series with a resistor.

This is already an application to dc generator. The problem required you to model the generator by a voltage source in series with a resistor. So, let's do what is being said. I have here the figure that shows the simple model mentioned in the problem in order to visualize it. I always love to draw the figure first when solving problems in electrical engineering. In the first place I'm a visual person. It's the easy way to understand what the problem is asking for.

With the circuit model of the generator shown above, I will defined the symbols as Vo for the dc generator voltage, I is the current, Rg is the series field connected to the dc generator and Vt is the terminal voltage or the generator output. Since there are two conditions mentioned above, let's expressed it in ohm's law for finding the dc generator voltage Vo which has no value given in the above problem and in terms of resistance which we also need to know here.

Therefore, we can state that: Vo = Vt + IRg

Condition 1 : Given that Vt = 115 V and I = 10 A
Vo = 115 V + (10 ) Rg, will served as equation 1.

Condition 2 : Given that Vt = 105 V and I= 15 A
Vo = 105 V + (15) Rg will served as equation 2.

Let's equate 1 and 2 since the value of Vo in equation 1 and 2 are equal. We can therefore expressed it mathematically as,

115 V+ 10Rg = 105 V + 15 Rg , we can now solve for Rg.

Rg = 2 ohms- answer

Then solving Vo will give, you may substitute the value of Rg from either equation 1 or 2 above will yield, I will choose equation 1.

Vo = 115 V + (10)(2) = 135 V - answer

These are some of the illustrative problems that I could share with you. on DC series Circuit Just always remember that when solving problems like what I illustrated above:

1. Try to make an simple illustration of the problem to picture out and understand the scenario of the problem.

2. Always try collect first the given data before proceeding in solving the problem.

3. There are some problems that you need to solved first the missing data before solving what was being required. Problem number 1 and 2 above are the best examples of this one.

4. Know what is the subject matter of the given problem is also one that you should not forget.

5. Always review and finalize your answers.

My next post will continue our study of Circuits connected in Parallel.

Hope you learned some tricks for today here in Learn Electrical Engineering for Beginners.

Cheers!

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DC Series Circuit Part 2

Hello folks, I'm glad that you're still there hunting for my new post here in our study of basic electrical engineering which is very recommended for the beginners. Well, if you find this site useful for you, then tell your friends and let them subscribe to my articles.

It's a little bit hectic on my work schedule including posting my blog here. Because I have to double my effort just for you... How sweet...I will not make my introduction again get longer because I know that you're really want to learn more here. So, let's continue of what we've left last moment which is the DC Series Circuit Part 1. For those who missed it, you can still catch up with the lecture.

Let's study the continuation...

The Voltage Division in the Series Circuit

In a series circuit, you would be able to find the voltage across at any point in the series circuit. The voltage which we called it the step-down voltage.

A circuit used for this is shown in the circuit diagram below. This is called a voltage divider. You may click the picture to enlarge.

Let's assume in the given circuit above that the applied voltage with the electrical notation of E or Ein is 100 volts and the values of R1 and R2 are 15 and 20 ohms respectively. You may want to know what is the applied voltage across R2 with the electrical notation of Vout or Eout which is written in another way. Please take note that the electrical notation of Vout or Eout could be an input voltage for another circuit. which of course will also become an Ein once more). That topic would be study on my succeeding post here in Electrical Engineering.

So, this is how you will going to do it...

We know that the total resistance in the circuit is 15 + 20 = 35 ohms. Given that the given circuit voltage is 100 volts. You may now use the Ohm's Law to find the circuit current. This is:

I = Ein / Rt = 100/35 = 2.86 amperes

Then, let's go to R2 in the given circuit. We all know that the resistance is 20 ohms and we have just calculated that the current is 2.86 amperes (from the conditions mentioned earlier in Ohm's Law Series Circuit that the current in the series circuit are just the same throughout).

Therefore, you will obtain that,

Eout = I x R2 = 2.86 x 20 = 57.2 volts - answer

You may observe that with the appropriate choice of resistor values in voltage divider chain, an input voltage of 100 volts has been stepped down to an output voltage of 57.2 volts. By using ohm's law, you would be able to calculate it.

Since we have an illustrative example above, let's expressed the above example into equation. Given that the total resistance is R1 + R2 and ohm's law tells you that the circuit current would be: Ein/ R1+R2. This is also the current across R2. Using Ohm's Law again, we can calculate the Eout = I x R2 will give an equation just by substitution:

Eout = (Ein/R1+R2) x R2

Expressing it in a correct and understandable way would give you...

Eout = (R1/R1+R2) x Ein

The equation above is the simplified formula that you can use in the given condition like this in voltage division chain. To put the equation into words. The voltage across any resistor in a voltage divider chain can be calculated by multiplying the value of that resistor by the input voltage dividedby the total resistance of the circuit.

Norton's and Thevenin's Theorem are commonly used principles when solving such voltage divider problems. This will be another basic concept that we will study on my succeeding post. For the meantime, let's absorbed first what we have now.

The Variable Resistors

You can also vary the resistance of the circuit as well. If you are not aware, you always done it by yourself by adjusting volume of your radio. This is what we called a variable resistor.

The resistor can be made variable in this way by means of sliding arm made of good conducting material to be arranged so that it can be moved along the length of the resistor. The resistor is then connected into the circuit with one of its end fastened to the sliding arm. By moving its sliding arm along the resistor, the value of the resistor can be varied at between maximum and minimum (zero).

If the variable resistor is used in this way, it is called the rheostat. It is used to control the current flow in the circuit.

The maximum value of resistance was obtained when the slider moves on the lower position as what had shown on the illustration above- left portion. (You may click the image to enlarge). Likewise, when the slider moves upward would obtain the minimum value of resistance. This is the simple function of a variable resistor.

A variable resistor may have either two or three circuit connections. The first picture that you see below is the example of the three terminal teminal connections variable resisitor which are commonly known as Potentiometer.

This is one typical sample for three terminal connections...

Typical potentiometer looks like this.

The Potentiometer Connections

The circuit diagram of a potentiometer is really no more than that of a voltage divider chain. R1-R2 is a single resistor effectively divided by the sliding arm C, whose movement alters the relative values of R1 and R2. Please refer to circuit diagram above.

The output voltage can vary from zero (when C is lowered so that R2=0) to full circuit voltage (when C is moved up so that R1=0)

Variable resistors, like fixed resistors, can be made with resistance material of carbon or can be wired-wound, depending on the amount of current to be controlled - wire-wound for large currents and carbon for small currents.

Wire-wound variable resistors are constructed by winding resistance wire on a porcelain or bakelite circular form, with a contact arm which can be adjusted to any position on the circular form by means of a rotating shaft. A lead connected to this movable contact can then be used, with one or both of the end leads, to vary the resistance used.

For controlling small currents, carbon variable resistors are constructed by depositing a carbon compound on a fiber disk. A contact on a movable arm actsto vary resistance as the arm shaft is rotated.

On my next post, let's have some practical applications for DC Series Circuit here in Learn Electrical Engineering for Beginners.

Cheers!

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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!

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Resistors Part 2- Color Code and How Resistance is Measured

Let's continue of what we have discussed yesterday before we go on the full discussion of a Series Circuit which will be our next topic that we will going to study here in Learn Electrical Engineering for Beginners.

Today, we will be dealing on how the resistor color coding is being used and how do we going to interpret it to obtain the reading. Then, afterward s we will touch a little bit on how the resistance is being measured. That's all will be discussed within this new post.

Let's begin now... timer start now!

The Resistor Color Code

We all know that we can find the resistance value of any resistor by using an ohmmeter. But what if we don't have an ohmmeter to use? Most of the case we can find the resistance value easier by interpreting its marking. Some resistors like wire-wound resistor have its printed value in ohms in their body. If they don't have the mark, you would require to use an ohmmeter. An example of a resistor which usually have all of the data printed directly on the resistor body with the information such as tolerance, temperature characteristics, and exact resistance value is the precision wire wound resistor. Other resistor like the carbon resistors usually do not have the data of characteristics directly marked on them, instead they have a so called color code by which they can be identified. You will wonder why it is being done this way for carbon resistors. The reason of using a color code for a carbon resistor is that they are small which is difficult to read the printed values especially when they are mounted.

Before we forgot something, there are two types of carbon resistors. The radial and an axial. They are only differ in the the way the leads are connected to the body of the resistor. Both employ the same color code but they are printed in the different manner. Radial lead resistors are not found in modern equipment. They are widely used in the past. I can't see any example of this now. Below is an example of an axial resistor.

In the picture above this axial lead resistors have its leads molded into the ends of the carbon rod of the resistor body. If you will see, the leads extends straight out in line from the body of the resistor. The carbon rod is coated with a good insulator.

Moving on...

Color coding system for resistors consists of three colors to indicate the resistance value in ohms of a certain resistor, sometimes the fourth color indicate the tolerance value of the resistor. By reading the color coded in correct order and substituting the correct value of each corresponding color coded as shown in the table below, you can immediately tell all you need to know about the resistor. The only thing that you will practice on how to use it and familiar yourselves for those value so that you can easily determine the value of the resistor color coded at a glance.

This is how you will do it.

The color of the first color band indicates the first digit of the resistance value or the first significant digit. Let's have an example below. Supposed that you have a given resistor below, the first color is yellow. If you would look at the table above it is equivalent to 4.

The second color coded of the resistor given below is violet, so this is now your second digit which is equivalent to 7 as shown in the table above.

The third color would served as your multiplier. In the case below since it is color red which is equivalent to 100 multiplier, or just simply add 2 zeros so this would look like this now:

47 ohm x 100 = 4, 700 ohms or 4.7 kilohms

Ooooppps! it seems that we are not done yet. The last color band or the fourth color band is gold which have 5% tolerance according to our table above. Therefore our final answer would be:

4.7 kilohms +/- 5% - answer

How to Measure the Resistance

We all know that voltmeter and ammeter are used for measuring the voltage and the current respectively. For the resistance, the meters that use to measure it is the ohmmeter. When using an ohmmeter, there should be no voltage present across the resistors except for the ohmmeter battery, otherwise your ohmmeter would be damaged. I can see two types of ohmmeter nowadays, the analog and the digital. Among the two ohmmeters, digital is widely used nowadays.

The above ohmmeter usually used to measure the resistance of the resistors. Ohmmeter ranges usually vary from 0-1,000 ohms to 0 -10 megohms. There are some special ohmmeters called the MEGGERS. This ohmmeter was used to measure high resistance values which are over 10 megohms. Some meggers use high voltage batteries and other use special type of hand generator to obtain the necessary voltage. These megohmeters is used to measure and test the resistance of insulation. Picture below is the example of a megger.

Ohmmeter is very easy to use by following two steps. First, the voltage must be set to the proper value. This is done with the zero adjustment by shorting outor by connecting together the two leads from the ohmmeter and setting to zero ohms on the meter with the zero adjustment control. This should be always done whenever you changed the meter range selector switch to a different scale. Now, the meter is now calibrated for the given range, you will notice that when the leads shorted out, the meter reads zero ohm, but when it opens, the meter reads infinity which indicates an open circuit. Therefore, when these leads touches the resistors subject for measurement, it will directly read the resistance in the meter multiplying it with the range selector switch. The range selector switch is serves as the multiplier or the multiplying factor whenever you are measuring the resistance using ohmmeter. The range selector switch usually marked as R, RX 10, RX 100, RX1,000, etc...
For example if the ohmmeter is switch on to R X 1,000 meaning the value of the meter will be multiplied to 1,000 to get the actual value of the resistance being measured.

That's it for today.

Tomorrow we'll continue dealing with circuits here in Electrical Engineering.

Cheers!

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Resistors Part 1 - Use and Properties

Now that you have learned the basic concept of Ohm's Law, we can now proceed in discussing the use, properties, and construction of resistors. All you can learn it here in Electrical Engineering.

Before we continue our study of circuits, we need to know more about resistance and resistors though we have touched it a little on my previous post. But its just a review. Today, it would be a bit deeper.

We know that there is a certain amount of resistance in all electrical equipment which we use. Sometimes, this resistance is not enough to control the flow of current to the extent desired. If you did not get my point here, let's have a few example of this. I will going to give an example by illustration as what had shown below. The circuit shown below, a switch and a current limiting resistor are used to control the flow of current through the motor. When starting a motor, the switch is kept open and the resistance is thereby added into the circuit to control the flow of current. After the motor has started, the switch is then closed in order to bypass the current limiting resistor.

There are wide variety of resistors, some of them have fixed values and some are variables.

What resistor is made up of?

Resistors are made up of special resistance wire, graphite (carbon) composition, or of metal film. Wire wound resistors are usually used to control large currents, while carbon resistors controls current which are relatively small.

Vitreous enameled wire-would resistors are constructed by winding resistance wire on a porcelain base, attaching the wire ends to metal terminals, and coating the wire and base with powdered glass and bake enamel to protect the wire and conduct heat away from it.

Fixed wire wound resistors with a coating other than vitreous enamel are also used. The example below is the example of this one.

Wire-wound resistors may have fixed taps, which can be also used to change the resistance value in steps, or sliders, which can be adjusted to change the resistance of any fraction of the total resistance. The picture below is the example of this one.

Precision wound resistors of manganin wire (a special wire that does not change resistance very much with high temperature) are used where the resistance value must be very accurate, such as in test instruments. The picture below is the example of this one.

Carbon resistors are used for low current applications. They are made from a rod of compensated graphite (carbon) that is mixed with clay and binders. By varying the amount of each component, it is possible to vary the resistance values obtained over a very wide range. Two lead wires are called pigtails are attached to the end of the resistance rod, and the rod is embedded in a ceramic or plastic covering, leaving the pigtails protruding from the ends. Take a look for a sample below.

You will find other type of resistor called a deposited film resistor used for special applications. These resistors are made by depositing a thin film of resistance metal or carbon on a ceramic core and then coating the resistor with either a ceramic or enamel protective coating. In many cases you will find that these resistors have radial leads meaning the leads come off at right angles to the body of the resistor. In some cases the deposited film is laid down on the core as spiral, similar to winding a wire around the tube, in order to increase the length of the resistance element without making the resistor too long. The example of this one was shown below.

Resistor Tolerance and Values

Let's consider this topic before we go on the color code for resistors. You need to find out the something about resistor tolerances and something about the preferred values of resistance that you will find in the circuits. Special resistors may have tolerances of as little as 1% , 0.1% or even 0.01% but most resistors that you will see have much greater tolerances. Large wire-wound resistors usually have tolerances of 10% or 5%. Carbon resistors are available in 20%, 10% and 5% tolerances.

So what are those tolerance mentioned above means? Let's take an example...

If you had a 10 kilohm resistor with a tolerance of 20%, the actual value of the resistor could anywhere from 10 kilohm - 10 kilohm (0.20) = 8 kilohm to 10 kilohm + 10(0.20) = 12 kilohm. That is how you will going to use the tolerance given for a specific resistor.

You will wonder how many different resistance values you can get for a resistor. It depends on the tolerance. Considerations such as this have led to the establishment of a set of preferred values of resistance in each tolerance where the highest tolerance of one value is about equal to the lowest tolerance of the next highest value. The table of preferred resistance was shown below. Later, you will find that resistors are available in different power ratings as well.

The numbers on the chart above show only the first two digits. Thus, it means for example, 33 means that 3.3, 330, 3.3 kilohm, 330 kilohm and 3.3 megohm resistors are available.

On my next post I will show you how the resistor color code is being used for carbon resistors and how the resistance is being measured.

I will tee off shortly. Stay more here in Learn Electrical Engineering for Beginners.

Cheers!

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