The subject of power in electrical systems is one of the most confusing and misunderstood concepts in circuit analysis, primarily because of how it is presented. Too often the instructor will lead to the final formulas with little or no regard to the justification of how they got there. Or they'll venture into the depths of sophisticated calculus losing the students in the process. In this presentation, you will find a comprehensive and complete lesson on the subject. It starts with a simple definition of power using simple terms and explanations. It moves through the subject of power analysis and electrical systems starting with DC circuits and ending with three phase power.
Using crisp, clean animated graphics, key formulas are derived using just enough intuitive logic to get there. When required simple algebra is used and required trigonometric functions are derived. Before using them. It is entirely you who will find the lessons in this journey enjoyable, and one you will keep for future reference. So sit back and enjoy the ride. Chapter one.
Energy is defined as the property that must be transferred to an object in order to perform work. energy equals work. Consider these two weight lifters lifting the same amount of weight to the same height. Both do the same amount of work. Both expend the same amount of energy in terms of physics, work equals mass times acceleration or gravity times height, which equals 100 kilograms times 9.8 meters per second squared times two meters which equals 1960. Jules.
However, the weightlifter on the left is slower than the weightlifter on the right. Hence we say that the right weight lifter is more powerful than the left weightlifter. Power measures the rate at which work is done. Or that power equals work divided by time. So if power is equal to work divided by time and we know that the same amount of work is done by each weightlifter because they've lifted the same weight through the same distance and that is equal to 1960 joules but the weightlifter on the left completes his lifts in three seconds. So the power delivered by that weightlifter is so 653 joules per second.
The weightlifter on the right however lifts his weight in one second. So that the power delivered by the right weight lifter is 1960 joules per second. Because work is measured in joules, power is measured in joules per second, and this measurement is defined as watts such that the work of one Joule completed in one second is equal to one watt. If we watch the lift, we see that the speed of the lift is not consistent. Regardless if the lift is completed in three or one seconds. Some of the lift is completed faster or slower than the other parts which means the power delivered will vary.
So, if we use the total time for the lift in our equation a one or the three seconds, we define that power, the power delivered as average power. If we break the whole lift up into smaller time increments, such as such that the power over that small increment is consistent. We will define that as instantaneous power which is consistent over that small time increment. In terms of electrical power, the work done or electrical energy is the movement of charges caused by the push of emf. In other words, it is the energy required to move an electric charge of q q looms over a potential difference of the volts and is expressed as V times q electron volts. By definition one electron volt is the amount of energy gained or lost by the charge of a single electron moving across an electric potential difference of one volt.
One Kunal is equal to 6250 followed by 15 zeros electrons, and one electron is equal to one over q, which is equal to 1.6 times 10 to the negative 19 kilo ohms. Electric power p is the rate at which electric energy is transferred by an electric circuit. The power p is the energy dissipated over time t, but the energy is equal to the voltage times the charge being passed. Therefore, Key is equal to the product of the voltage times the charge all over T or voltage times q divided by T. And because Q divided by T is I or current, where one amp is equal to one coulomb of electrons passing by in one second of time, P is given by the voltage times the current, for a constant voltage and constant current or DC values for voltage and current, or it might be considered the product of the instantaneous voltage times the instantaneous current.
Electrical power is measured in watts. A watt, sometimes symbolized by the capital letter W. is a derived unit of power in the International System of Units si. This is a chart of the International system of units for power. The most common ones that are used are the milli watt, which is point 000001 of a lot, or 10 to the minus six watts, or a kilowatt, which is 1000 watts or 10 to the third watts or a megawatt, which is 1 million watts, or 10 to the six watts, or a gigawatt which is 1000 megawatts, or 10 to the ninth watts. Now, the power of a circuit and the voltage and the current are related by these equation which is the same equation just written three different ways. And you can memorize the relationship by the above triangle.
You can see that P is always over either V or AI, depending on what you're looking for if you're looking for V voltage than its power over AI, if you're looking for current, then it's p all over V. The most common one used is the first one course powers equal to the voltage times the current. But AI is used is equal to P over V is used all the time in calculating the current draw on electrical circuits and electricians use this when contemplating or designing the circuits for house wiring say. Here's an example. an electrician may want to put in a 1500 watt heater or a 1.5 kilowatt heater, and he's supplying that heater at 240 volts. He wants to know what type of fusing to use for that. And if you do the calculation of P over V, you can see that it'll draw 6.25 amps for one heater or 12.5 amps for two heaters.
If he uses a 20 amp fuse circuit, he'll be drying 63% of the fuse rating, which is quite alright. However, if he was contemplating using a 15 amp fuse for two heaters, they would be drawing at 3% of a 15 amp fuse rating, which would exceed 3% above what the regulations call for in fusing for those heaters. So that's the formula that you would use in calculating current draws in any type of a circuit. Reviewing with energy is defined as the ability to do work. electrical energy is energy transferred to an electrical load by a moving electrical charge over a period of time. It is also equal to the amount of power that is delivered during a period of time.
In other words, energy is equal to power times time. This is defined as a joule or a watt second, however, watt seconds are very small and because they are very small energy is also measured in much larger units such as a watt hour or a kilowatt hour. Now, this is how an energy company or a utility bills their electrical customers. Certainly, residential customers are charged for the amount of energy that flows into their house and the energy meter on the house is actually calculating the amount of power that's delivered over a period of time, which the utility converts into a A financial charge that they charge the customer in building large industrial customers. There's another way of calculating the power but it also includes the calculation of energy. There'll be more on this in the next couple of slides.
This is a chart of the International System of Units si for electrical energy, the most common of which are the milliwatt hour, which is equal to point 000001 or 10 to the minus six watt hours, the kilowatt hour which is 1000 watt hours or 10 to the third watt hours or a megawatt hour which is 1 million watt hours or 10 to the six watt hours. For varying current and voltage, it helps to talk in terms of instantaneous power and average power. average power we'll deal with a little bit later. For now instantaneous power is the power delivered over a very short period of time, and can be expressed as p instantaneous is equal to the instantaneous times I instantaneous for each instant of time if graphed over a very short period of time. And as you can see here, if we make that slice of a very short period of time, very, very small, then the voltage the instantaneous voltage and instantaneous current is steady over that very short period of time.
So our equation of power is equal to voltage times current holds true. Let's now look at all terminating current and voltage, the alternating current and voltage that we will be concentrating on for this course is described as sinusoidal and looks like this. Both the voltage and current vary over time as a sine wave. utilities in power companies generate their power in this form for various reasons, which we won't go into at this time. However, suffice to say that the voltage that's generated and the current is usually in a sinusoidal manner like this, the current and voltage will vary from a positive maximum value to negative maximum value. When we plot the power you will notice that although vn IR sinusoidal and pass through zero from positive to negative values, power is always positive for in phase voltage and current When we multiply negative voltage and negative current The answer is positive.
You will notice that P is also sinusoidal PS frequency is double that of the N di In other words, it's two times V and I and the power p is always greater than zero if the current and voltage are in face. This ends the chapter