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1.3 Electrical Charge

Physicists often resort to models and theories to describe and represent some force that can be measured in the real world. But very often these models and representations are no more than concepts that fail to physically represent the object. In this sense, no one knows exactly what gravity is, or what is an electrical charge. Gravity, which can be felt and measured, is the force between masses.

By the same token, bodies in "certain electrical conditions" also exert measurable forces on one another. The term "electrical charge" was coined to explain these observations.

Three simple postulates or assumptions serve to explain all electrical phenomena:

1.Electrical charge exists and can be measured. Charge is measured in Coulombs, a unit named for the French scientist Charles Agustin Coulomb.

2.Charge can be positive or negative.

3.Charge can neither be created nor destroyed. If two objects with equal amounts of positive and negative charge are combined on some object, the resulting object will be electrically neutral and will have zero net charge.

1.3.1 Voltage

Objects with opposite charges attract, that is, they exert a force upon each other that pulls them together. In this case, the magnitude of the force is proportional to the product of the charge on each mass. Like gravity, electrical force depends inversely on the distance squared between the two bodies; the closer the bodies the greater the force. Consequently, it takes energy to pull apart objects that are positively and negatively charged, in the same manner that it takes energy to raise a big mass against the pull of gravity.

The potential that separate objects with opposite charges have for doing work is called voltage. Voltage is measured in units of volts (V). The unit is named for the Italian scientist Alessandro Volta.

The greater the charge and the greater the separation, the greater the stored energy, or voltage. By the same token, the greater the voltage, the greater the force that drives the charges together.

Voltage is always measured between two points that represent the positive and negative charges. In order to compare voltages of several charged bodies a common reference point is necessary. This point is usually called "ground."

1.3.2 Current

Electrical charge flows freely in certain materials, called conductors, but not in others, called insulators. Metals and a few other elements and compounds are good conductors, while air, glass, plastics, and rubber are insulators. In addition, there is a third category of materials called semiconductors; sometimes they seem to be good con-

Where P represents the power in watts, V is the voltage in volts, and I is the current in amperes. Ohm's Law can also be formulated in terms of voltage, current, and resistance as shown later in this chapter.

1.4 Electrical Circuits

An electrical network is an interconnection of electrical elements. An electrical circuit is a network in a closed loop, giving a return path for the current. A network is a connection of two or more simple elements, and may not necessarily be a circuit.

Although there are several types of electrical circuits they all have some of the following elements:

1.A power source, which can be a battery, alternator, etc., produces an electrical potential.

2.Conductors, in the form of wires or circuit boards, provide a path for the current.

3.Loads, in the form of devices such as lamps, motors, etc., use the electrical energy to produce some form of work.

4.Control devices, such as potentiometers and switches, regulate the amount of current flow or turn it on and off.

5.Protection devices, such as fuses or circuit breakers, prevent damage to the system in case of overload.

6.A common ground.

Figure 1-5 shows a simple circuit that contains all of these elements.

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Figure 1-5 Simple Circuit

1.4.1 Types of Circuits

There are three common types of circuits: series, parallel, and series-parallel. The circuit type is determined by how the components are connected. In other words, by how the circuit elements, power source, load, and control and protection devices are interconnected. The simplest circuit is one in which the components offer a single current path. In this case, although the loads may be different, the amount of current flowing through each one is the same. Figure 1.6 shows a series circuit with two light bulbs.

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Figure 1-6 Series Circuit

In the series circuit in Figure 1-6 if one of the light bulbs burn out, the circuit flow is interrupted and the other one will not light. Some Christmas lights are wired in this manner, and if a single bulb fails the whole string will not light.

In a parallel circuit there is more than one path for current flow. Figure 1-7 shows a circuit wired in parallel.

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Figure 1-7 Parallel Circuit

In the circuit of Figure 1-7, if one of the light bulbs burns out, the other one will still light. Also, if the load is the same in each circuit branch, so will be the current flow in that branch. By the same token, if the load in each branch is different, so will be the current flow in each branch.

The series-parallel circuit has some components wired in series and others in parallel. Therefore, the circuit shares the characteristics of both series and parallel circuits. Figure 1-8 shows the same parallel circuit to which a series rheostat (dimmer) has been added in series.

VARIABLE RESISTOR (DIMMER)

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Figure 1-8 Series-Parallel Circuit

In the circuit of Figure 1-8 the two light bulbs are wired in parallel, so if one fails the other one will not. However, the rheostat (dimmer) is wired in series with the circuit, so its action affects both light bulbs.

1.5 Circuit Elements

So far we have represented circuits using a pictorial style. Circuit diagrams are more often used since they achieve the same purpose with much less artistic effort and are easier to read. Figure 1-9 is a diagrammatic representation of the circuit in Figure 1-8.

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Figure 1-9 Diagram of a Series-Parallel Circuit

Certain components are commonly used in electrical circuits. These include power sources, resistors, capacitors, inductors, and several forms of semiconductor devices.

V

V=IR

I R

V

I=V/R

I R

V

R=V/I

I R

Figure 1-10 Ohm's Law Pyramid

A popular mnemonics for Ohm's Law consists of drawing a pyramid with the voltage symbol at the top and current and resistance in the lower level. Then, it is easy to solve for each of the values by observing the position of the other two symbols in the pyramid, as shown in Figure 1-10.

1.5.3 Resistors in Series and Parallel

When resistors are in series the total resistance equals the sum of the individual resistances. The diagram in Figure 1-11 shows two resistors (R1 and R2) wired in series in a simple circuit.

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Figure 1-11 Resistors in Series

In Figure 1-11 the total resistance (RT) is calculated by adding the resistance values of R1 and R2, thus, RT = R1 + R2.

In terms of water flow, a series of partially closed valves in a pipe add up to slow the flow of water.

Resistors can also be connected in parallel, as shown in Figure 1-12.