Chapter One, power and energy. We're going to start the course off with an understanding of just what is power and energy and how it's related to electrical systems. Once we've established the basis for power and energy measurement in electrical system we will go on to study, single and three phase metering systems. Energy is defined as a property that must be transferred to an object in order to perform work. energy equals work and work equals energy. Consider these two weight lifters lifting the same amount of weights through the same 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 gravity times height. And in this case, it's 100 kilograms times 9.8 meters per second squared, which is gravity's acceleration times two meters, which equals 1960. jewels. 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 being done.

Or that power equals work divided by time, where time is the interval it takes to lift the weight from the floor to its final Height if the left weightlifter completes his lift in three seconds, and the right weight lifter completes his lift in one second. The power delivered by the left weightlifter is 653 joules per second and the power delivered by the right weightlifter is 1960 joules per second, the same amount of work is done, but at a different times and by different powers. 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 one or three seconds, we define that power delivered as average power. If we break the whole lift up into smaller time increments such that the power over that small increment is consistent. We can define what is known as instantaneous power, which is consistent over the small time increments. Now we'll talk a little bit more about this when we start to study how it applies to electrical systems, but for now, we are just defining average power which is the power delivered over a larger period of time or instantaneous power which is delivered over a very small increment of time. In terms of electrical power, the work done or electrical energy is the movement of charges caused by a push of emf. In other words, it is the energy required to move an electric charge of two kilos over a potential difference of the bolts.

And it is and it 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 bolt. Remember that one coudl is equal to 6250 With 15 zeros after it electrons or one electron is equal to one over q, which is equal to 1.6 times 10 to the negative 19 kilo ohms. Power is the rate at which electrical energy is transferred by an electric circuit. Power is the energy dissipated over time, which is T, but e is equal to v times q therefore, p is equal to the product of the times q all over T or V times q divided by T and because Q divided by T is current, designated by I, one amp equals one Kunal move electrons passing by one second in one second of time, then P is the times I or the voltage times the current constant voltage in constant currents such as in DC power, this holds true.

Electric Power is measured in watts a watt symbolized by the letter W is a derived unit of power in the international system units. Si, named after the Scottish engineer James walk, this is a chart of the International System of Units for power, the most common of which are the milli watt, which is 10 to the negative six watts. A kilowatt which is 1000 or 10 to the third power watts, a megawatt which is 1 million or 10 to the six power watts, or a gigawatt which is 10 to the ninth power watts. Now, power is given by the product of voltage times the current. But if you are given any one of these two quantities that are used to calculate power power being one of them and voltage and current being the other two, given any two you can always calculate the third power of course, is equal to the voltage times the current.

But if you know the power and you know the current that's delivered, but delivering that power, then you can calculate the voltage across the load by power divided by current or if you know the, the power and you know the voltage across the load, then you can calculate the amps that is flowing to that power. Reviewing energy it is defined as the ability to do work. electrical energy is the energy to transferred to an electrical load by moving electrical charges over a period of time. It is also equal to the amount of power that is applied during a period of time. That is energy is equal to power times time. This is defined as a joule.

But because the Joule is so small energy is also measured in much larger units such as the watt hour and the kilowatt hour. When calculating energy or electrical energy, electrical energy is equal to the voltage times the electric current times the time interval. Energy is equal to the four volts times I for amps times t in seconds, or in abbreviated terms, e is equal to v times i times t But we know that power p is equal to the times or the voltage times the current. Therefore, energy may be defined in terms of the power over a period of time or E is equal to P times t. This is a chart of the International System of Units for electrical energy, the most common of which are the milliwatt of power which is 10 to the minus six watt hours, the kilowatt hour which is 1000 or 10 to the third power watt hours and the megawatt hour which is equal to 1 million or 10 to the six power watt hours.

For varying current and voltage, it helps you talk in terms of instantaneous power and average power. average power we will deal with later but for now, instantaneous Power is the power delivered over a very short period of time t, and can be expressed as P sub i is equal to V sub i times i sub vi for each instant of time, if graphed over a very short period of time. Now let's look at alternating current and voltage. The alternating current and voltage that we will concentrate on for this metering course is described as sinusoidal. And it looks like this. Both voltages and current vary over time, like a sine wave.

Shown here they're both shown as being in phase. They the current and voltage vary from positive maximum value to a negative maximum value. When we Plot power, you will notice that V times V and AI are sinusoidal and pass through zero from positive to negative. Power is always positive though, when we multiply a negative voltage and a negative current, the answer is positive. So you will notice that the power is also sinusoidal. The powers frequency is two times the frequency of the of I. and p is always greater than zero if current and voltages are in phase.

Remember our plot of steady voltage and current and power. If we were to plot the steady power consumption p on a graph over a period of time and shade the area under peak it would look like this P times t, the total energy consumption would be the area of the rectangle given by the formula, E for energy is equal to P times t. Another way of looking at energy is the area defined by P and T. Now, if we divided up the big rectangle into a series of little rectangles, the area would be the same, and the defined energy would still be the same. And the areas of each of the smaller rectangles would be given by p times delta t. And now collectively, the energy would be given by the sum of all the little P times delta T's which would be sum up to the big area P times t. Now for the moment, let's assume that the power consumption is not steady, but might look something like this.

And the areas of each of the smaller rectangles would would still be given by p times delta t. and collectively, the energy over that period of time would be given by the sum of all the P times delta T's. Now, let's suppose the power does not change in steps, but in a smooth curve, such as shown here, we can approximate the area under the curve by a set of rectangles, with Delta T's identical and whose vertical power p is bounded by the curve. If we decrease the time sections or the Delta T's to a very small value, they're thereby increasing the number of P times t rectangles. Well, each p remains on the curve, then our total areas would be the total area would be exactly the area bounded by the curve. So if we're able to capture the area bounded by the curve, it would be that of the energy delivered to the load.

This is precisely what kilowatt hour meters do. This is the end of chapter one.