What Is Electric Power?

If we are going to recall our Physics subject, it is said that whenever a force is applied that causes motion the work is said to be done. Take a look on the illustration below:


Forces that work is done and  forces not doing work.

The first figure shown above are combination of forces which work is done and forces which work is not done. (a)The picture in which the shelf is held under tension does not cause motion, thus work is not done. (b) The second picture in which the woman pushes the cart causes motion, thus the work is done. (c) The man applied tension in the string is not working since as there is no movement in the direction of the force. (d) The track applied horizontal force on the log is doing work.

The potential difference between any two points in an electric circuit, which gives rise to a voltage and when connected causes electron to move and current to flow. This is one of a good example in which forces causing motion, thus causing work to be done.

Talking about work in electric circuit, there is also a electric power which is the time rate of doing work done of moving electrons from point to point. It is represented by the symbol P, and the unit of power is watt, which is usually represented by the symbol W. Watt is practically defined as the rate at which work is being done in a circuit in which the current of 1 ampere is flowing when the voltage applied is 1 volt.

The Useful Power Formula

Electric Power can be transmitted from place to place and can be converted into other forms of energy. One typical energy conversion of electrical energy are heat, light or mechanical energy. Energy conversion is what the engineers really mean for the word power.

The power or the rate of work done in moving electrons through a resistor in electric circuit depends on how many electrons are there to moved. It only means that, the power consumed in a resistor is determined by the voltage measured across it, multiplied by the current flowing through it. Then it becomes,

Power = Voltage x Current
Watts  = Volts x Amperes

P = E x I  or P = EI ------> formula no.1

The power formula above can be derived alternatively in other ways in terms of resistance and current or voltage and resistance using our concept of Ohm's Law. Since E=IR in Ohm's Law, the E in the power formula above can be replaced by IR if the voltage is unknown. Therefore, it would be:

P = EI
P = (IR)I or P = I²R ------------> formula no.2

Alternatively if I = E/R in Ohm'Law, we can also substitute it to E in the power formula which is terms of voltage if the resistance is unknown.

P = EI
P = E(E/R) or P = E²R ---------> formula no. 3

For guidance regarding expressing of units of power are the following:
a. Quantities of power greater than 1,000 watts are generally expressed in (kW).
b. Quantities greater than 1,000,000 watts are generally expressed as megawatts (MW).
c.  Quantities less than 1 watt are generally expressed in (mW).

The Power Rating of Equipment

Most of the electrical equipment are rated in terms of voltage and power - volts and watts. For example, electrical lamps rated as 120 volts which are for use in 120 volts line are also expressed in watts but mostly expressed in watts rather than voltage. Probably you would wonder what wattage rating all about.

The wattage rating of an electrical lamps or other electrical equipment indicates the rate at which electrical energy is changed into another form of energy, such as heat or light. It only means the greater the wattage of an electrical lamp for example, the faster the lamp changes electrical energy to light and the brighter the lamp will be.

The principle above also applies to other electrical equipment like electric soldering irons, electrical motors and resistors in which their wattage ratings are designed to change electrical energy into some forms of energy. You will learn more about other units like horsepower used for motors when we study motors.

Take a look at the sizes of carbon resistors below. Their sizes are depends on their wattage rating. They are available with same resistance value with different wattage value. When power is used in a material having resistance, electrical energy is changed into heat. When more power are used, the rate at which electrical energy changed into heat increases, thus temperature of the material rises. If the temperature of the material rises too high, the material may change it composition: expand, contract or even burn. In connection to this reason, all types of electrical equipment are rated for a maximum wattage.


Carbon resistors with comparative sizes of different wattage ratings
of 1/4 watt, 1/2 watt,1 and 2 watts

If the resistors greater then 2 watts rating are needed, wire-wound resistors are used. They are ranges between 5 and 200 watts, with special types being used for power in excess of 200 watts.



Use wire wound resistors if higher than 2 watts are needed

Fuses

We all know that when current passes through the resistors, the electrical energy is transformed into heat which raises the temperature of the resistors. If the temperature rises too high, the resistor may be damaged thereby opening the circuit and interrupting the current flow. One answer for this is to install the fuse.

Fuses are resistors using special metals with very low resistance value and a low melting point. When the power consumed by the fuses raises the temperature of the metal too high, the metal melts and the fuse blows thus open the circuit when the current exceeds the fuse's rated value. What is the identification of blown fuse? Take a look on the picture below.



This is the good fuse



This is the blown fuse

In other words, blown fuses can be identified by broken filament and darkened glass. You can also check it by removing the fuse and using the ohmmeter.

There are two types of fuses in use today - conventional fuses, which blow immediately when the circuit is overloaded. The slow-blowing (slo-blo) fuses accepts momentary overloads without blowing, but if the overload continues, it will open the circuit. This slo-blo fuses usually used on motors and other appliances with a circuit that have a sudden rush of high currents when turned on.

Fuses are rated in terms of current. Since various types of equipments use different currents, fuses are also made with different sizes, shapes and current ratings.

Various types of fuses are made for various equipments

Proper rating of fuse is needed and very important. It should be slightly higher than the greatest current you expect in the circuit because too low current rating of fuse will result to unnecessary blowouts while too high may result to dangerously high current to pass.

Later we will be study circuit breaker which is another protective devices for over current protection.


Electrical Power in Series, Parallel and Complex Circuits

The principle of getting the total power of the circuit is just simple. There is no need to elaborate this topic.

The total power consumed by the circuit is the sum of all power consumed in each resistance.

Therefore, we just only sum up all power consumed in each resistance whether it a series, parallel or a complex circuits. Thus,

P_t= P₁+P₂+P₃+P_n watts  ---------->formula no. 4

From the problem in my previous post about complex circuit, try to calculate each power of the resistance and the total power as well. Constant practice always makes you perfect!

Cheers!

On 23:41 by Admin

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Solution To Brain Teaser Number 1

As I promised last time, I will give you the detail solution to our brain teaser on my previous post here in Learn Electrical Engineering for Beginners. So for those who are not yet through, you can still catch up.

Let's proceed to solved our first problem here with this topic.

Last time, this is the worded problem I had given to you.

Problem No.1 : A process equipment contains 100 gal of water at 25 degree celcius. It is required to bring it to boiling in 10 minutes. The heat loss is estimated to be 5%. What is the KW rating of the heater?

Here's the solution:

Since, we have given the mass of water subject for boiling ( 100 degree celcius) = 100 gal. I would like to convert it to gram so that our units are compatible when we substitute it with our general formula.

Given that, 1 gal = 3.786 liters and 1 liter of water is equivalent to 1kg. We can therefore convert it:

100 gal x 3.786 liters /1 gal x 1 liter/ 1 kg = 378.6 kg of water. But since I would like to convert it to gram. It is therefore equivalent to 378,600 grams. The specific heat of water is 1cal/g-C.

In our Heat Formula, we all know that it is,

Qo = mc delta T

Qo = 378, 600 ( 1 cal/g-C) ( 100-25 ) = 28395000 cal or 28,395 kcal

Let : Wo = Qo; where Wo = energy out

but 4, 186 joules = 1 kcal

Wo = 28, 395 kcal ( 4, 186 joules/ 1 kcal) = 118,861,470 joules

In order to get the energy in of the process equipment, we will be needing the formula below to get it:

Win = Wo/ %n, which comes from the efficiency formula. This formula will be touched in various topic here in Electrical Engineering course.

Substituting the values that we have will lead to:

Win = 118,861,470 joules / (1- .05) = 125,117,336.8 joules or 125.117 x 10 ^6 joules.

We are not yet through with our answer. The problem is asking for the KW rating of the equipment. In our previous formula of Power = Energy ( joules) / Time ( seconds). Since, the water will be boiled for 10 minutes as what stated in the above problem. It is therefore,

Rating of Equipment (KW) = 125, 117, 336.8 joules / 600 seconds ( in 10 minutes)

Rating of Equipment (KW) = 208, 529 watts or 208. 529 KW - ANSWER

Notice that I did not used rounded values in my substitution. I only rounded it off in my final answer because in board exams, multiple choice answers are very near with each other. Rounding off numbers while you are still in the process of computing will take a little difference in final answer. For you to get the accurate and exact number, I advice you to round off your numbers in your final answer only.

I hope you had learned something here today. Please catch me more here in Learn Electrical Engineering for Beginners. I'll be back shortly.

Cheers!

On 19:55 by Admin

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Voltage, Current, Power and Energy

Let's begin with the very basic concept of Electrical Engineering. We should do this because as we move along, we will use these basic concepts on more complicated applications. The following topics were already taken from our Physics course but for those who already forget it, let's take a short review.

The Voltage

We all know that Potential Difference between two points is the work done per unit charge when a charge is moved from one point to the other. The defining equation for this is,

V = W/Q

where :

V = the voltage in volts.

W= energy in joules.

Q = is the charge in coulombs, is always understood to be a positive charge in a conventional way, thus making definite the algebraic sign of the potential difference in any particular case.

One volt is defined as the potential difference between points in an electric circuit such that one joule of work must be done to move a charge of one coulomb between the points considered. Since the difference of potential between two points is expressed in volts, the potential difference is often referred to as voltage between these points. Thus, if an electric power line has a voltage of 220V, it follows that 220J of work have to be expended for each coulomb of electricity which is transferred through any apparatus connected between the two wires. The statement above could be shown in a simple expression as:

1 volt = 1 joule/coulomb, or 1 V = 1 J/C

Actually, voltage is being measured using the instrument called the voltmeter. There, you can see the actual voltage reading between two terminals of the actual circuit for example of a television sets, radio and other electronic /electrical instruments. If you have your Physics Laboratory before it was supposed to be tackled.

I hope you get my point here. I will not give much details about this topic above as well as the topics to be discuss below because this is just a review of your Physics. We only need to remember important concepts now just to be ready on the more complicated one. You have to trust me on this for the meantime.

The Current

Let's take an example of a light bulb connected to the battery source. A voltage source such as battery, that forces electric charge to move through the rest of the circuit from one terminal of the voltage source back to the other and an unbroken path through the rest of the circuit along which the charge can move. The charge that moves through this circuit is called an electric current. This is also defined in the other way around as the rate of charge flow of one coulomb per second.

Mathematically, this can be expressed as:

I = Q/t

where:

I = the current in amperes.

Q= the charge in coulombs.

t = the time in seconds.

Here in electrical engineering, we will be dealing with two types of current: the direct current and an alternating current. This is a huge topic to be discuss separately on my succeeding post because the idea is completely separate. Just to give you a little background about this. Take for example of a light bulb connected to the battery source. The current produced by the battery is one typical example of a direct current. When a direct current flows, charge always move in the same direction - electrons move away from the negative terminal of the emf source toward the positive terminal. Those other electronics devices that are connected to the terminals of the wall socket oscillate back and forth at 60Hz. The voltage across the wall socket in a home changes polarity at a frequency of 60Hz ( 60 times per second). This is a typical example of an alternating current.

Common instrument used to measure an electric current in an electric circuits is an ammeter.

Power and Energy

The property of the body or system of bodies by virtue of which work can be performed is called energy. Commonly defined as "ability to do work". Energy can exist in many forms and can be tranformed from one form to another. One of these energy that we will considered here in Electrical Engineering is the heat.

Heat is defined as the energy transferred to or from an object because of a difference in its temperature and that of some other object in contacts in its environment.

Mathematically, this is expressed as:

Q = mc delta T

where:

Q = heat in kcal

m = mass

C = specific heat

delta T = change in temperature

Always take note that, 1 kcal is the amount of heat required to raise the temperature of 1-kg of water by 1 degree celcius.

Update August 6, 2008: Don't forget to review the value of specific heat for every substance for you will used it in problem solving in the last part of this post.

Power is restricted to mean the time rate of doing work. The average power is the worked performed divided by the time required for the performance. Mathematically, this is expressed as:

P = W/t = VI

where:

P = the power in watts

W= the energy in joules

t = the time in seconds

Please take note that all units above are expressed in MKS. This is the commonly unit being used nowadays especially in board examinations.

A Teaser

Here in Electrical Engineering, there is no challenge if I will not leave any problem solving to my readers. For you to fully digest the topic presented here, please try to solve the problem below. Answers will be given before posting my next post and will be found on the separate page of this site. The problem below was given during Registered Electrical Engineering board exams dated October, 1997.

Problem No.1 : A process equipment contains 100 gal of water at 25 degree celcius. It is required to bring it to boiling in 10 minutes. The heat loss is estimated to be 5%. What is the KW rating of the heater?

Please stay with me on my next post here in Learn Electrical Engineering for Beginners.I will reveal the solution on my next post. Goodluck!

Cheers!

On 19:49 by Admin

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