11.2: Electrical Fundamentals

What is Electricity?

Electricity is a form of energy that powers the devices and machines we use every day, like the lights in our homes, the television, and the computer you might be using right now. It's created when charged particles (electrons) move through a conductor, like a wire. We can control the flow of these electrons with various devices, including: resistors, capacitors, and transistors, to perform specific tasks such as generating light, heat, and motion.

Think of it like water flowing through a hose. The water represents the electrons, and the hose represents the wire. We can turn the hose on and off with a valve, just like we can control the flow of electricity with a switch. And just as the water can power a sprinkler or a water wheel, electricity can power all sorts of devices and machines.

A basic electrical system consists of sources and loads. A source is the device that creates the energy, this can be a battery, a 120 volt wall outlet, or any number of electrical generators such as a solar panel. A device that converts (consumes) the power from an electrical source to another source of energy is an electrical load. Examples of common loads are lights, heaters, motors, fans, and even computers.

Electrical systems are powered through one of two distinct types of systems, Alternating Current (AC) and Direct Current (DC).

AC is a type of electrical current that regularly changes direction think of it like pushing power, then pulling power), typically at a frequency (Hz) of 50 or 60 times per second. AC power is used to power most of the electrical devices we use in our homes, such as lamps, televisions, and appliances. AC power is generated by power plants and is distributed to homes and businesses through power lines. In the United States, most household electrical systems run on 120 Volts.

DC on the other hand, is a current that flows in one direction only. Electricians use DC to power devices that require a steady and constant flow of electricity, such as batteries, electronics, and electric vehicles. DC power can be generated by batteries or by converting AC power using a device called a rectifier.

The characteristics of AC and DC power are different. AC power can travel long distances with minimal power loss, making it well-suited for use in power grids. AC power is also relatively easy to transform into different voltages, which is important for distributing power to different areas. However, AC power is more complex to generate than DC power and can be more dangerous as it is often used at very high voltages. DC power is also easier to store in batteries, which is important for portable and off-grid applications. However, DC power is far less efficient than AC power for transmitting electricity over long distances because the wires have to be larger to carry a lower voltage.

The power formula

When dealing with high voltage applications, which is most of what we work with in theatre, an especially useful formula is the power formula. Power is a measure of the rate at which energy is transferred or used over time. Larger devices require more power than smaller ones. We can understand the relationships of power measurements by using the power formula. \(W=VA\) represents the relationship between power (W), voltage (V), and current (A) in an electrical circuit. In order to use the power formula, we must first understand its variables:

• Power = Watts (W). Watts measure the rate at which energy is transferred or used over time. One watt is defined as the amount of power required to do one joule of work per second. To use the water flow analogy, power is the amount of water required to make a device work, similar to the flow of a shower head.
• Electrical Potential = Volts (V). Volts measure the electrical potential energy per unit of charge in an electrical circuit. It is the force that drives the flow of electric charge in a circuit. To use the water flow analogy again, voltage can be thought of as the "pressure" that drives the flow of electricity in a circuit.
• Current = Amps (A). Amps represent the rate at which electrical charge flows through a circuit. The higher the current, the greater the amount of electric charge flowing through the circuit per unit of time. To use the water flow analogy, current is the speed at which the water flows.

Power Formula

\[W = VA \nonumber\]

\[V = \frac{W}{A} \nonumber\]

\[A = \frac{W}{V} \nonumber\]

The power formula is remarkably simple, \(W=VA\). We often remember it by singing the words “West Virginia.” If we only know two of the variables, it can be rearranged to solve for any missing information.

Example \(\PageIndex{1}\)

Let’s say that we know the rating of our electrical outlet and want to know how many lights it can safely support. Let’s fill in what we know: 1) in the US, most household outlets are 120 Volts, 2) after inspecting the circuit breaker panel, we see that the outlet is rated to 15 Amps. Let’s use the power formula to find out what power that outlet is rated to?

Solution

\[W = VA \nonumber\]
\[W = 120 \times 15 \nonumber\]
\[W = 1,800 \nonumber\]

After using the power formula, we find that the outlet can safely support no more that 1,800 Watts of power. That would be one 1,000W light, three 500W lights, or 18 100W lights.

American Wire Gauge and Safe Wire Loads

The United States and Canada use the American Wire Gauge (AWG) system to categorize the sizes and power ratings of commercially available wires. We can convert AWG sizes into the metric system of mm², for use throughout the rest of the world, but for our purposes we will use this American standard. The AWG system consists of numerical values that describe wire diameter. In general, larger wire diameters are able to handle greater electrical currents. While there are many tables describing wire gauge capacity for varying applications, below is a table that shows a simplified relationship between AWG and wire capacity in Amps for use in theatre.

Gauge of Wire	10	12	14	16	18
Capacity in Amps	25	20	15	6	3

Notice that a smaller wire gauge has a greater capacity in amps. This is because the smaller the gauge number, the larger the physical wire. Let’s use this table in combination with the power formula to reveal the smallest safe cable size for a given application.

Example \(\PageIndex{2}\)

Assume you have a 1,200W theatre spotlight on a standard 120V electrical service. What is the smallest safe wire gauge you can use to power the light? Let’s use the power formula to find the light’s required current, in Amps.

Solution

\[W = VA \nonumber\]
\[1,200 = 120 \times A \nonumber\]
\[\frac{1,200}{120} = \frac{120 \times A}{120} \nonumber\]
\[10 = A \nonumber\]

Using the table above, the smallest wire gauge that can safely transmit 10 Amps is a 14 gauge cable. Choosing a cable any smaller could lead to a cable melting, starting a fire, or worse.

Types of circuits

There are two basic types of electrical circuits used to distribute electricity: series and parallel. A third more common circuit is the combination circuit which is a combination of both series and parallel.

Figure \(\PageIndex{3}\): The three types of circuits

Series Circuit: A series circuit is a circuit in which the electrical components, such as resistors or light bulbs, are connected in a single loop or chain, with the same current flowing through each component. The total resistance of a series circuit is equal to the sum of the individual resistances of the components. In a series circuit, if one component fails or is removed, the entire circuit is broken and no current will flow.

Parallel Circuit: A parallel circuit is a circuit in which the electrical components are connected in multiple branches, with the voltage across each component being the same. The total resistance of a parallel circuit is less than the resistance of any individual component. In a parallel circuit, if one component fails or is removed, the other components continue to operate normally.

Combination Circuit: Perhaps the most common circuit used in theatre equipment, a combination circuit is a circuit that combines elements of both series and parallel circuits. In a combination circuit, electrical components are connected in both series and parallel configurations. The behavior of a combination circuit can be analyzed by breaking it down into smaller sections and analyzing each section separately, then combining the results.