### Current

All batteries have two terminals, a positive and a negative one. On a flashlight battery, for example, one end (usually marked with a + sign) is the positive terminal, and the other end (usually marked with a – sign) is the negative terminal.

When a battery is connected to a load with wires, the potential difference, or voltage, between the two terminals (the two opposite charges) forces a third charge to move. The charge in motion is called an electric **current**. Current is produced when a potential difference moves an electric charge. Picture a battery connected with wires to a light bulb:

The battery produces a voltage, which forces the free electrons in the wire to move. The mobile free electrons moving in the wire are the current. The current is always a continuous flow of electrons, and at every point in the circuit, the current is the same.

Load:the resistance in an electric circuit.

Electric current is measured in amperes. An **ampere** is defined to be 6.25 × 10^{18} electrons moving past any given point in one second. This is the same as one coulomb of charge moving past any given point in one second. The symbol for current is **I** or **i**. Mathematically, current is expressed as:

- I = where I is current in amperes (A), Q is charge in coulombs (C), and T is time in seconds (s).

*Example*: What is the current if 10 coulombs of charge flow through a light bulb every 5 seconds?

The charge, or number of electrons, can be determined using the equation above:

- I =

- multiply both sides of the equation by time

Therefore, if we solve for charge, or Q, this same equation tells us that charge is equal to current multiplied by time. In other words, charge equals the amount of current during a given time period.

*Example:* How many electrons are flowing through the light bulb when the current is 2 amperes?

### Alternating Current (AC) and Direct Current (DC)

A battery is an example of a direct voltage source. The terminals of the battery always maintain the same polarity, so the current flow from one terminal to the other is always in the same direction. On the other hand, an alternating voltage source periodically reverses its polarity. The current resulting from an alternating voltage also periodically changes its direction of flow.

The electricity generated in a power plant is by nature an alternating voltage. The magnetic fields developed in a rotating turbine always produce an alternating voltage. The voltage we most often use in our homes is 110 volt 60 Hz. The 60 Hz, or Hertz, refers to the frequency that an alternating voltage changes polarity. In this case the polarity changes from positive to negative and back to positive 60 times a second.

One advantage of producing an alternating voltage is that it is more easily changed to a different value than a direct voltage can be changed. This is very important because power plants produce thousands of volts, while we can safely use just 110 or 220 volts in our homes. Most of our appliances then convert the 110 or 220 volts to even a smaller voltage. Simple transformers are used to step up or down alternating voltages. A direct voltage must first be converted to an alternating voltage before its value can be changed. This adds complexity and cost to using direct voltages.

Another benefit of using alternating voltages and currents is that they can be easily and inexpensively converted into direct voltage and current. A diode is a semiconductor device that allows current to flow in only one direction.When the direction of current flow changes, the diode acts like an insulator and stops the current. Two or four diodes can be used to transform alternating voltages and currents into direct voltages and currents. This process is referred to as **rectifying** an alternating voltage.

Basic electrical theory is most easily understood by studying direct voltages and currents. The study of alternating voltages and currents can become very complex. The rest of this chapter will discuss only direct voltages and currents.

### Conductors, Insulators, and Semiconductors

A copper wire is an example of a conductor. A **conductor** is a material that has electrons that can easily move.Metals are very good conductors. Copper is used to make most of the wires we use because it has high conductance and is relatively inexpensive. Aluminum was used in the 1950s to make wires for our homes because it was less expensive than copper; however, it is not as good a conductor.

An **insulator** is a material whose electrons do not move freely. Glass, rubber, wood, and porcelain are all examples of insulators. Insulators are used to prevent the flow of current.

A **semiconductor** is a material that conducts less than a metal conductor but more than an insulator. Silicon is the most recognized semiconductor. Most transistors, diodes, and integrated circuits are produced from semiconductor materials such as silicon or germanium.

### Resistance

**Resistance** is the opposition to current. A copper wire has very little resistance; therefore it is a good conductor. Insulators have a large resistance. The symbol for resistance is **R**. Resistance is measured in **ohms**. The symbol for ohms is the Greek letter omega, Ω. The schematic symbol for resistance is:

A good copper wire has a resistance of about onehundredth of an ohm, or 0.01 Ω per foot. For comparison, the resistive heating element used in a medium-size hair dryer has a resistance of about 14 Ω.

Resistors are fabricated using many different materials. The most common types of resistors are wire-wound resistors, carbon-composition resistors, and film resistors.Wire-wound resistors are generally used in high-power applications. Carbon resistors are the most common. They are used in most electronic circuits due to their low cost. Carbon resistors can't typically be built with an exact resistance value. Film resistors are used when a more exact resistance is needed. Resistors are easily built with resistance values from 0.01 Ω to many millions of ohms.

### Analog Electrical Circuits

All electrical circuits have the three following components:

- A potential difference or voltage.
- A closed path for current to flow from one side of the potential difference to the other.
- Resistance, which is often referred to as a "load."

Ohm's law defines the relationships between voltage, current, and resistance in a simple electrical circuit.

The illustration below shows a flashlight, where the voltage source is a battery and the load is a lightbulb:

Ohm's law states that:

- potential difference (or voltage) = current × resistance

or

- V = I × R

This can be rewritten as:

*Example:* The battery in the flashlight below supplies 4.5 volts and the light bulb has a resistance of 1.5 Ω. How much current flows in the circuit?

Ohm's law states that current (remember that current is measured in amperes) equals voltage over resistance:

According to Ohm's law, 3 amperes of current flows through this circuit.

### Series Resistance Circuits

Multiple resistance elements may be used in an electric circuit. An example of this type of circuit is the *series* resistance circuit, as represented schematically below:

R_{1} and R_{2} are both in the same current path, providing more total resistance than a single resistance element. It is crucial to remember, however, that in a series resistance circuit, the current is the same everywhere in the circuit. In other words, the current flowing through R_{1} is the same as the current through R_{2}. The total circuit resistance is the sum of the resistance of each individual resistance element.

*Example*: Christmas tree lights are a good example of a series resistance circuit. The following circuit represents four bulbs in a string connected to a 20-volt source; each bulb provides 5 ohms of resistance. What is the current flowing through the string of lights?

Again, Ohm's law states that the current equals the voltage over the resistance, and in this circuit the total resistance is equal to the sum of the resistance of each of the four bulbs.

The voltage across each of the light bulbs in the example above can also be easily calculated using Ohm's law:

- V

_{1}= I × R

_{1}

- V

_{1}= 1 A × 5 Ω

- V

_{1}= 5 V

Notice that the sum of the voltages across each bulb equals the total voltage. This can be stated:

- V

_{T}= V

_{1}+ V

_{2}+ V

_{3}+ V

_{4}

or

- V

_{T}= 5 V + 5 V + 5 V + 5 V

- V

_{T}= 20 V

### Parallel Resistance Circuits

A **parallel** resistance circuit has two or more loads connected across a single voltage source. An example of this is plugging your coffee pot and toaster into the same electric outlet. Consider the circuit below, where R_{1} is the coffee pot and R_{2} is the toaster.

The **voltage** across each resistor of a *parallel* resistance circuit is the same. On the other hand, the **current** through each resistor of a *series* resistance circuit is the same. The current through each resistor in a *parallel* circuit may be different, depending on the resistance of the loads. The total current of the circuit is the sum of the current through each resistor.

- I

_{T}= I

_{1}+ I

_{2}

Again, the voltage across both R_{1} and R_{2} is the same, it is V. The current through each resistor can still be calculated using Ohm's law.

*Example*: What is the total current, I_{T}, that a 120-volt source must supply if a coffee pot with a resistance of 30 ohms and a toaster with a resistance of 20 ohms are plugged into the same outlet?

The total current:

The resultant total resistance of the toaster and coffee pot is the value a single resistor would have if the toaster and coffee pot were combined. Look at the previous example and determine the total resistance. The total resistance is equivalent to the total voltage divided by the total current; therefore, using the coffee pot and toaster:

We can redraw our circuit now with a single load replacing the coffee pot and toaster. Notice that the equivalent resistance of 12 Ω is indeed less than the resistance of either the toaster or coffee pot.

Electrical circuits many times combine series and parallel resistance. Determining the total current depends on first solving for the total resistance. The parallel resistances must first be combined and then added to the series resistance to determine the total resistance.

Ohm's law in a parallel resistance circuit really means that the voltage is constant and the total current is the sum of the currents through each resistor. Ohm's law in a series resistance circuit implies that the current is constant and the total voltage is the sum of the voltages across each resistance.

### Electrical Power

The measurement of **power (P)** should be familiar to everyone. Light bulbs are used according to their wattage. Electrical power is measured in **watts (W)**. A watt is defined to be the work done in one second by one volt to move one coulomb of charge. It is written mathematically:

Remember that current is:

- I =

Substitute I for into the equation above to give:

- P = V × I

This is called the power equation; power, or the number of watts, is equal to voltage multiplied by current.

Watt:the work done in one second by one volt to move one coulomb of charge.

*Example*: Calculate how many watts a light bulb uses when it is connected to a 120-volt circuit with 0.5 A flowing.

- P = V × I

- P = 120 V × 0.5 A

- P = 60 watts

One of the most important circuit characteristics an electrical designer must consider is the power dissipated in a resistor when current flows through it. A resistor will heat up when current flows. The heat is equivalent to the power lost in the resistor. We can use the power equation (P = V × I) and Ohm's law to determine the power dissipated in a resistor.

When we substitute Ohm's law into the power equation to calculate power in terms of current:

- P = V × I

Ohm's law is V = I × R. Substitute (I × R) for V in the power equation giving:

- P = (I × R) × I

- P = I

^{2}R

We can also use Ohm's law to solve the power equation in terms of voltage:

- P = V × I

Ohm's law is I = . Substitute for I in the power equation giving

The heat generated in a resistor is sometimes harmful and sometimes beneficial. When too much power is lost in a resistor, it can burn up and destroy an appliance. A toaster is an example of using the heat generated in a resistor for benefit. The heating element in a toaster is nothing more than a large resistor.

*Example*: How much power does the heating element of the toaster use in the following circuit?

### Miscellaneous Electrical Components

### Capacitors

Most practical circuits contain devices other than voltage sources, resistors, and wires. Capacitors, for instance, are widely used. A capacitor is an electrical device that can store electrical charge. A capacitor's function is limited to AC circuits. A common application for capacitors is building filter circuits to protect appliances from voltage spikes. The symbol for a capacitor (C) is similar to a voltage source.

### Fuses

Fuses are used to protect almost every electrical item we use. A **fuse** is typically a small piece of wire that will burn up and stop conducting electricity when too much current is forced to flow through it. Fuses are rated to blow at a given current, up to a maximum voltage. For example, a typical fuse in a television may be rated to blow, or open, at 3.0 amperes at any voltage up to 120 volts to protect the television from currents over 3 amperes and voltages over 120 V. An ideal fuse has zero resistance of its own and opens instantly when excess current flows. Some fuses are designed to allow a large current surge to safely flow for a small period of time. This is important because many appliances and motors have what is called an in-rush current surge. A "**slo-blo**" fuse will allow a large current to flow for a few seconds before opening.

### Switches

Most circuits wouldn't be practical if we couldn't turn them on and off. **Switches** are used to break a circuit path to stop current flow to a load, such as a lightbulb. There are many types of switches, depending on the application. The most common switches are singlepole- single-throw and double-pole-double-throw switches. The dial used to turn the channel on older televisions is a called a rotary switch. A rotary switch opens and closes contacts when it is turned.

### Electronic Manufacturing and Testing

A common workshop will have most of the tools needed to work on electrical equipment. Pliers, screwdrivers, wire cutters, and wrenches are all needed. In addition, a few specialty tools are required. For instance, a wire stripper is a very useful tool. It is used to remove the insulation from a wire in preparation for joining the wire to a circuit element.

### Solder

Solder and a soldering iron are used to physically connect most circuit components. **Solder** is a metal alloy usually containing almost equal amounts of tin and lead. Solder is usually specified to be either 40 percent tin and 60 percent lead, 50 percent each, or 60 percent tin and 40 percent lead. The latter mixture does the best soldering job because it melts the easiest, flows the best, and hardens the fastest. However, it is more expensive than the other mixtures. A soldering iron melts solder by heating it to 500 or 600 degrees Fahrenheit; the solder is fused to the metal leads of the electronic components and wires as it cools to permanently bond them together. A joint that has been properly soldered will appear shiny and smooth. A flux must also be used when soldering to remove oxidation from the components to be joined. The flux is typically contained in the solder. One must be careful to not use acid flux when joining electronic components because the acid will eventually corrode the solder joint. A rosin flux is preferred for electronic uses.

### Wires and Printed Circuit Boards

Wires have historically been used to connect the components of a circuit. Today's modern technology has replaced most wires with **printed circuit boards (PCBs)**. Printed circuit boards are thin, typically fiberglass boards with electronic components soldered to them and copper circuit paths, called traces, that replace discrete wires. Complex circuits can be built using multi-layer PCBs. The copper traces can be sandwiched and laminated between more boards. Typical multi-layer circuit boards may have three to seven layers of circuit paths. If you take the top off a computer or television you will see large and small PCBs and relatively few discrete wires. Wires are mostly used today to join PCBs to connectors.

## Mastering Zeros

The numbers used for circuit analysis are often either very large or very small. Writing out all the zeroes before or after the decimal point can be extremely tedious. Prefixes are used to simplify the writing out of all the zeros.

For example a billion words can be written as any of the following:

1,000,000,000 words

or

1,000 million words

or

1 × 10

^{9}wordsor better yet

1G words

The following table lists the prefixes that are typically used to simplify measurement terminology.

prefixsymbolmultipliergiga G 109 mega M 106 kilo k 103 milli m 10 ^{–3}micro u 10 ^{–6}nano n 10 ^{–9}pico p 10 ^{–12}