In the office, hospital, and home, we are surrounded by equipment, appliances, and many other devices powered by electricity. Although knowledge of electricity and electronics is not needed to watch television, talk on the telephone, or use a toaster, these examples are just the tip of the electrical and electronic iceberg in the world we live in as electromyographers.

One might ask, is it really necessary to understand the basics of electricity and electronics in order to perform routine electrodiagnostic (EDX) studies? Although a degree in electrical engineering certainly is not needed, the answer clearly is yes. First, and most important, understanding the basics of electricity is essential to safely perform EDX studies and prevent potential electrical injuries to patients (see Chapter 40 ). Second, all of the responses recorded during nerve conduction studies and needle electromyography (EMG) are small electrical signals that are amplified, filtered, and then displayed electronically. Knowledge of electricity and electronics allows for a better understanding of what these potentials represent. Finally, and equally as important, knowledge of electricity and electronics is critical to understand and correct the variety of technical problems that frequently arise during EDX studies (see Chapter 8 ).

## Basics of Electricity

All atoms have a nucleus composed of positively (+) charged particles, *protons *, and particles with no charge, *neutrons *. Orbiting around the nucleus are negatively (−) charged particles, *electrons *. Most atoms have the same number of protons and electrons; the electrons remain bound in their orbit by their magnetic attraction to the protons (i.e., in magnetism, opposites attract).

Electricity is formed when electrons are removed from their orbit and flow to adjacent atoms. Materials that allow electrons to move freely are known as *conductors *. In contrast, materials that inhibit the flow of electrons are known as *insulators *. Conductors typically are metals, most often copper. Insulators most often are rubber, plastic, or ceramic. To understand basic electrical circuits, one needs first to be acquainted with several important terms:

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is the standard unit of electric charge, approximately equal to 6.24 × 10**Coulomb**^{18 }electrons.

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, represented by the symbol**Current**, is the actual flow of electrons. The ampere is a measure of current, designated by the letter**I**. An**A**is defined as 1 coulomb passing a point in a conductor in 1 second. Current can only flow when a complete circuit exists.**ampere**

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is the electromotive force required to make electricity flow through a conductor. This electromotive force results from a fundamental property of magnetism that oppositely charged particles attract each other. Any source with an excess of electrons (negatively charged particle) will be drawn to a source with a lack of electrons (positively charged particle). Voltage is designated by the symbol**Voltage**. Its unit of measurement is**E**, which is designated by the letter**volts**.**V**

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opposes the flow of electrons. Resistance is designated by the symbol**Resistance**. The unit of measurement for resistance is**R**, which is designated by the Greek letter**Ohms**. All materials, even conductors, impede the flow of electrical current to some extent. In general, resistance increases with the length of the conductor and decreases as the cross-section of the conductor increases.**Ω**

## Analogy between Electricity and Water

Because current and electrons cannot be seen, it may be difficult to relate to electricity and its basic definitions. One useful way of understanding electricity and its properties is to make an analogy to the flow of water. The analogy to water and plumbing often is easier to grasp and can be extrapolated to the understanding of electricity.

Water can be measured as a specific volume (e.g., a liter or gallon). Thus, a gallon of water is analogous to a coulomb of electricity, an amount of charge. For water to flow, it must have some force that is driving or pushing it. This force can be gravity, in the case of water stored in a water tower, or a pump that mechanically propels the water. In either case, water is put under pressure. Pressure is measured as force per unit area, typically as pounds per square inch (psi). Thus, water pressure is analogous to voltage, the driving electromotive force. Water will flow if there is a pressure difference between two points (i.e., from an area of high pressure to low pressure). Likewise, electrons will flow if there is a difference in voltage between two points. Flow is the actual movement of water, which is measured as volume passing by a point in a specific time period (e.g., gallons per second). Thus, flow of water is analogous to current, the movement of electrons, which is measured in amperes (1 coulomb passing a point in a conductor in 1 second). Lastly, resistance to water flow is determined by the physical characteristics of the pipes it is traveling through. Longer and especially narrow-diameter pipes impede the flow of water. Thus, the mechanical resistance of a water pipe is analogous to the electrical resistance of a circuit.

The flow of water is determined by *Poiseuille’s law *:

At point D in the figure above, the water pressure is essentially zero. Water is taken up by the pump and pressurized, resulting in a high pressure at point A. Water will now flow because it is under high pressure at point A and low pressure at point D. The water pressure at point B will still be high because the diameter of the pipe is so large that it offers little resistance to flow. However, the marked narrowing of the pipe between points B and C increases the resistance to flow. The higher the resistance, the less the flow. Conversely, the higher the water pressure difference, the more the flow. At point C, the water pressure is now very low. However, it must still be slightly higher than point D so that water will flow from point C to D. If extra water were to somehow get into the system and be a greater amount than the water pump could pump, it could easily be diverted to the reservoir (analogous to the * ground *, see later).

## Ohm’s Law

The most important basic principle of electricity is *Ohm’s law *, which defines the relationship among current, voltage, and resistance in a circuit. Ohm’s law is directly analogous to Poiseuille’s law for water. *For electrical circuits, Ohm’s law states that: *

The figure above depicts a simple circuit consisting of a battery ( *E *) (an electromotive source of electrons) connected to one resistor ( *R *). The amount of current ( *I *) flow is determined by Ohm’s law, *I *= *E */ *R *, where *E *is the voltage from the battery, and *R *is the resistance. Also note the presence of the ground connection. The ground is ideally a true electrical zero. Most often true grounds are physically connected to the earth (e.g., through a pipe).

One of the confusing aspects of electricity is figuring out the direction that current actually flows. In the *conventional flow notation *, electric charges move from the positive (surplus) side of the battery to the negative (deficiency) side. However, as electricity comes about by the flow of electrons, which are negatively charged, the actual flow of electrons occurs from the negative to the positive. In the *electron flow notation *, electric charges moves from the surplus of negative charges at the negative side of the battery to the positive side of the battery which has a deficiency of negative electrical charges. Both notations are correct when used consistently. The conventional flow notation is used by most electrical engineers and found in most electrical engineering textbooks, and will be used in this chapter.

One helpful aid in remembering the relationships in Ohm’s law is the Ohm’s triangle illustration (above). If a triangle is constructed with *E *at the top and *I *and *R *at the bottom as shown, the value of *E *, *I *, or *R *can readily be determined by blocking the variable of interest (shaded in the figure) and looking at the relationship between the other two parameters.

## Kirchhoff’s Laws

In addition to Ohm’s law, there are two other important principles, known as *Kirchhoff’s laws *, with which one must be familiar in order to understand basic electricity.

*Kirchhoff’s current law states that the algebraic sum of all the currents meeting at any point in a circuit must be zero. *Put another way, the sum of incoming currents must equal the sum of outgoing currents. This law represents the conservation of charge. The number of electric charges that flow toward a point must equal the number of electric charges that flow away from that point.

*Kirchhoff’s voltage law states that, in a closed circuit, the algebraic sum of all the voltage (i.e., potential) drops is equal to the electromotive source voltage of the circuit. *The figure above shows a battery with a voltage ( *V *_{A }) connected in series to three resistors (B, C, D). The current running through the three resistors results in a voltage drop across each resistor, *V *_{B }, *V *_{C }, and *V *_{D }, respectively. Kirchhoff’s voltage law requires that the sum of the voltage drops across all three resistors equals the voltage of the battery (i.e., *V *_{B }+ *V *_{C }+ *V *_{D }= *V *_{A }).

## Simple Resistive Circuits

## Resistors in Series

From Ohm’s and Kirchhoff’s laws, one can predict the behavior of simple resistive circuits.

First, take the example of a simple circuit with a battery ( *E *) connected to three resistors in series. From Kirchhoff’s current law, the current ( *I *) must be the same going through each resistor (i.e., current flowing into any point equals the current flowing out of that point). From Ohm’s law, a voltage drop will be present across each resistor ( *E *= *I *× *R *). Thus, the voltage drops for the three resistors must be *I *× *R *_{1, }*I *× *R *_{2 }, and *I *× *R *_{3 }, respectively. From Kirchhoff’s voltage law, the voltage from the battery ( *E *) must equal the sum of all the voltage drops across the three resistors ( *V *_{B }+ *V *_{C }+ *V *_{D }). With this information, applying simple algebra:

*E*=*V*_{B }+*V*_{C }+*V*_{D }(Kirchhoff’s voltage law)

*E*=*I*×*R*_{1 }+*I*×*R*_{2 }+*I*×*R*_{3 }(Ohm’s law)

*E*=*I*× (*R*_{1 }+*R*_{2 }+*R*_{3 }) (Algebra)

*E*=*I*×*R*(Ohm’s law)

*R*=*R*_{1 }+*R*_{2 }+*R*_{3 }(Algebra, using substitution)

*Thus, resistors in a series can be directly added together to calculate a net resistance. *Take an example of the same circuit of a battery connected to a series of three resistors, using real values.

The battery has a voltage of 100 V. The resistors have a resistance of 12, 10, and 3 Ω, respectively. Thus, the total resistance of the circuit is the sum of the resistors (12 + 10 + 3) = 25 Ω. With this information, the current can be easily calculated from Ohm’s law:

Knowing the current, the individual voltage drop across each resistor (48 V, 40 V, 12 V) can be calculated from Ohm’s law ( *E *= *I *× *R *).

## Resistors in Parallel

When resistors in a circuit are placed in parallel, a net resistance can also be calculated using Ohm’s and Kirchhoff’s laws.

Take an example of a simple circuit with a battery ( *E *) connected to three resistors in parallel. From Kirchhoff’s current law, the total current ( *I *) must be the sum of the individual currents going through each resistor:

From Ohm’ law, the voltage across each resistor can be calculated:

From Kirchhoff’s voltage law, the voltage from the battery must equal the voltage drops along any closed circuit. Thus, the same voltage ( *E *) from the battery must be present across each of the three resistors:

With this information, we can solve the equation for total current:

Now, we can solve for the total resistance:

Thus, resistors in parallel reduce the total resistance, as opposed to resistors in series, which increase the total resistance. For instance, three resistors in series, each 100 Ω, result in a total resistance of 300 Ω. However, three resistors in parallel, each 100 Ω, result in a net resistance of 33 Ω. The analogy to water is as follows. Imagine a bucket full of water. The weight of the water creates a water pressure against the bottom of the bucket. If a hole is drilled through the bottom of the bucket, water will start to flow, based on how large the hole is (i.e., the resistance) and the water pressure in the bucket. If another hole is drilled nearby (i.e., in parallel), there are now two ways for water to escape (under the same pressure), and hence the amount of water leaving the bucket (i.e., the current) will increase. Thus, the two holes in parallel effectively decrease the resistance to water leaving the bucket.

## Direct Current and Alternating Current

* Direct current *(DC) is current that always flows in the same direction. In DC, electrons flow uniformly from the power source through a conductor to a load (i.e., an electrical device) and back to the power source. The most common example of a DC power source is the battery.

However, current also can be supplied as an * alternating current *(AC). In an AC, electrons follow the path of a sine wave, flowing first in one direction and then reversing. The current reverses polarity many times a second [measured as cycles per second (cps) or Hertz (Hz)]. The most common example of AC is the conventional 60 Hz electricity in wall sockets in houses and offices.