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The Fundamentals: [What is Alternating Current?] [Resistors and AC] [Capacitors and AC] [Inductors and AC] [Transformers and AC] [Diodes and AC]
Resistance and Reactance: [Series RC Circuits] [Series RL Circuits] [Parallel RC Circuits] [Parallel RL Circuits] [Series LC Circuits] [Series RLC Circuits] [Parallel LC Circuits] [Parallel RLC Circuits]
Filter Concepts: [Filter Basics] [Radians] [Logarithms] [Decibels] [Low-Pass Filters] [High-Pass Filters] [Band-Pass Filters]
Power Supply Fundamentals: [Elements of a Power Supply] [Basic Rectifier Circuits] [Filters] [Voltage Multipliers]
What is Alternating Current?

### Alternating Current vs. Direct Current

The figure to the right shows the schematic diagram of a very basic DC circuit. It consists of nothing more than a source (a producer of electrical energy) and a load (whatever is to be powered by that electrical energy). The source can be any electrical source: a chemical battery, an electronic power supply, a mechanical generator, or any other possible continuous source of electrical energy. For simplicity, we represent the source in this figure as a battery.

At the same time, the load can be any electrical load: a light bulb, electronic clock or watch, electronic instrument, or anything else that must be driven by a continuous source of electricity. The figure here represents the load as a simple resistor.

Regardless of the specific source and load in this circuit, electrons leave the negative terminal of the source, travel through the circuit in the direction shown by the arrows, and eventually return to the positive terminal of the source. This action continues for as long as a complete electrical circuit exists.

Now consider the same circuit with a single change, as shown in the second figure to the right. This time, the energy source is constantly changing. It begins by building up a voltage which is positive on top and negative on the bottom, and therefore pushes electrons through the circuit in the direction shown by the solid arrows. However, then the source voltage starts to fall off, and eventually reverse polarity. Now current will still flow through the circuit, but this time in the direction shown by the dotted arrows. This cycle repeats itself endlessly, and as a result the current through the circuit reverses direction repeatedly. This is known as an alternating current.

This kind of reversal makes no difference to some kinds of loads. For example, the light bulbs in your home don't care which way current flows through them. When you close the circuit by turning on the light switch, the light turns on without regard for the direction of current flow.

Of course, there are some kinds of loads that require current to flow in only one direction. In such cases, we often need to convert alternating current such as the power provided at your wall socket to direct current for use by the load. There are several ways to accomplish this, and we will explore some of them in later pages in this section.

### Properties of Alternating Current

A DC power source, such as a battery, outputs a constant voltage over time, as depicted in the top figure to the right. Of course, once the chemicals in the battery have completed their reaction, the battery will be exhausted and cannot develop any output voltage. But until that happens, the output voltage will remain essentially constant. The same is true for any other source of DC electricity: the output voltage remains constant over time.

By contrast, an AC source of electrical power changes constantly in amplitude and regularly changes polarity, as shown in the second figure to the right. The changes are smooth and regular, endlessly repeating in a succession of identical cycles, and form a sine wave as depicted here.

Because the changes are so regular, alternating voltage and current have a number of properties associated with any such waveform. These basic properties include the following list:

• Frequency. One of the most important properties of any regular waveform identifies the number of complete cycles it goes through in a fixed period of time. For standard measurements, the period of time is one second, so the frequency of the wave is commonly measured in cycles per second (cycles/sec) and, in normal usage, is expressed in units of Hertz (Hz). It is represented in mathematical equations by the letter 'f.' In North America (primarily the US and Canada), the AC power system operates at a frequency of 60 Hz. In Europe, including the UK, Ireland, and Scotland, the power system operates at a frequency of 50 Hz.
• Period. Sometimes we need to know the amount of time required to complete one cycle of the waveform, rather than the number of cycles per second of time. This is logically the reciprocal of frequency. Thus, period is the time duration of one cycle of the waveform, and is measured in seconds/cycle. AC power at 50 Hz will have a period of 1/50 = 0.02 seconds/cycle. A 60 Hz power system has a period of 1/60 = 0.016667 seconds/cycle. These are often expressed as 20 ms/cycle or 16.6667 ms/cycle, where 1 ms is 1 millisecond = 0.001 second (1/1000 of a second).
• Wavelength. Because an AC wave moves physically as well as changing in time, sometimes we need to know how far it moves in one cycle of the wave, rather than how long that cycle takes to complete. This of course depends on how fast the wave is moving as well. Electrical signals travel through their wires at nearly the speed of light, which is very nearly 3 × 108 meters/second, and is represented mathematically by the letter 'c.' Since we already know the frequency of the wave in Hz, or cycles/second, we can perform the division of c/f to obtain a result in units of meters/cycle, which is what we want. The Greek letter (lambda) is used to represent wavelength in mathematical expressions. Thus,  = c/f. As shown in the figure to the right, wavelength can be measured from any part of one cycle to the equivalent point in the next cycle. Wavelength is very similar to period as discussed above, except that wavelength is measured in distance per cycle where period is measured in time per cycle.
• Amplitude. Another thing we have to know is just how positive or negative the voltage is, with respect to some selected neutral reference. With DC, this is easy; the voltage is constant at some measurable value. But AC is constantly changing, and yet it still powers a load. Mathematically, the amplitude of a sine wave is the value of that sine wave at its peak. This is the maximum value, positive or negative, that it can attain. However, when we speak of an AC power system, it is more useful to refer to the effective voltage or current. This is the rating that would cause the same amount of work to be done (the same effect) as the same value of DC voltage or current would cause. We won't cover the mathematical derivations here; for the present, we'll simply note that for a sine wave, the effective voltage of the AC power system is 0.707 times the peak voltage. Thus, when we say that the AC line voltage in the US is 120 volts, we are referring to the voltage amplitude, but we are describing the effective voltage, not the peak voltage of nearly 170 volts. The effective voltage is also known as the rms voltage.

When we deal with AC power, the most important of these properties are frequency and amplitude, since some types of electrically powered equipment must be designed to match the frequency and voltage of the power lines. Period is sometimes a consideration, as we'll discover when we explore electronic power supplies. Wavelength is not generally important in this context, but becomes much more important when we start dealing with signals at considerably higher frequencies.

### Why Use Alternating Current?

Since some kinds of loads require DC to power them and others can easily operate on either AC or DC, the question naturally arises, "Why not dispense entirely with AC and just use DC for everything?" This question is augmented by the fact that in some ways AC is harder to handle as well as to use. Nevertheless, there is a very practical reason, which overrides all other considerations for a widely distributed power grid. It all boils down to a question of cost.

DC does get used in some local commercial applications. An excellent example of this is the electric trolley car and trolley bus system used in San Francisco, for public transportation. Trolley cars are electric train cars with power supplied by an overhead wire. Trolley busses are like any other bus, except they are electrically powered and get their power from two overhead wires. In both cases, they operate on 600 volts DC, and the overhead wires span the city.

The drawback is that most of the electrical devices on each car or bus, including all the light bulbs inside, are quite standard and require 110 to 120 volts. At the same time, however, if we were to reduce the system voltage, we would have to increase the amount of current drawn by each car or bus in order to provide the same amount of power to it. (Power is equal to the product of the applied voltage and the resulting current: P = I × E.) But those overhead wires are not perfect conductors; they exhibit some resistance. They will absorb some energy from the electrical current and dissipate it as waste heat, in accordance with Ohm's Law (E = I × R). With a small amount of algebra, we can note that the lost power can be expressed as:

Plost = I²R

Now, if we reduce the voltage by a factor of 5 (to 120 volts DC), we must increase the current by a factor of 5 to maintain the same power to the trolley car or bus. But lost power is a function of the square of the current, so we will lose not five times as much power in the resistance of the wires, but twenty-five times as much power. To offset and minimize that loss, we would have to use much larger wires, and pay a high price for all that extra copper. A cheaper solution is to mount a motor-generator set in each trolley car and bus, using a 600 volt dc motor and a lower-voltage generator to power all the equipment aboard that car.

The same reality of Ohm's Law and resistive losses holds true in the country-wide power distribution system. We need to keep the voltage used in homes to a reasonable and relatively safe value, but at the same time we need to minimize resistive losses in the transmission wires, without bankrupting ourselves buying heavy-gauge copper wire. At the same time, we can't use motor-generator pairs all across the country; they would need constant service and would break down far too often. We need a system that allows us to raise the voltage (and thus reduce the current) for long-distance transmission, and then reduce the voltage again (to a safe value) for distribution to individual homes and businesses. And we need to do this without requiring any moving parts to break down or need servicing.

The answer is to use an AC power system and transformers. (We'll learn far more about transformers in a later page; for now, a transformer is an electrical component that can convert incoming AC power at one voltage to outgoing power at a different voltage, higher or lower, with only very slight losses.) Thus, we can generate electricity at a reasonable voltage for practical AC generators (sometimes called alternators), then use transformers to step that voltage up to very high levels for long-distance transmission, and then use additional transformers to step that high voltage back down for local distribution to individual homes.

In practice, this is done in stages. The really high-voltage transmission lines hanging from long glass insulators on the arms of tall steel towers carry electricity cross-country at several hundred thousand volts. This is stepped down to about 22,000 volts for distribution to multiple neighborhoods — these are the wires you see at the top of the telephone poles in many areas. Additional transformers mounted on some of these telephone poles step this voltage down again for distribution to several homes each.

The design of the system minimizes the overall cost by balancing the cost of transformers against the cost of heavier-gauge copper wire, as well as the cost of maintaining the system and repairing damage. This is how the cost of electricity delivered to your home or business is kept to a minimum, while maintaining a very high level of service.

### A Note on Nomenclature

When we examined DC circuit theory and discussed DC power losses above, we used capital letters to represent all quantities. This is standard nomenclature; capital letters are used to represent fixed, static values. Thus, we use a capital I to represent DC current and a capital V to represent DC voltage.

By the same token, we use the capital letters R, L, and C to represent the values of circuit components containing resistance, inductance, and capacitance, respectively. These are fixed values that are set at the time the component is manufactured.

On the other hand, AC circuits use constantly-changing voltages and currents. In addition, some circuits contain both AC and DC components, which must often be considered separately. Therefore, we typically use lower-case letters to designate instantaneous values of voltage, current and power. Thus, if you see an equation written as:

P = I × E

you know it refers to DC power, current, and voltage. On the other hand, an equation written as:

p = i × e

refers to the instantaneous power, current, and voltage of some AC signal at some specified instant in time.

There will also be cases where we must refer to an overall AC signal rather than one instantaneous value from it. In such cases, the use of upper- and lower-case letters may be adjusted so we don't have too many of one or the other in a single discussion. We will try to avoid unnecessary confusion by including subscripts in equations, or specifying in the text exactly what we are discussing.

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