Before you start working with circuits, you need to understand the
main concepts upon which the core of electrical engineering lies.
Understanding the basics will help you keep up with the material and
reduce the number of errors you make in the future. While there are
some very important equations that you need to know, circuit analysis is
not simply a matter of plugging numbers into an equation. You need to
understand what voltage, current, and resistance is, and how they relate
to each other in order to take advantage of those equations and
understand what’s really going on in the circuit. This article will
introduce you to the most basic concepts.
Engineering Notation
In this course and many other courses in the department, we want you
to work with engineering notation. Scientific notation is useful for
very small or
very large
numbers. However, you should use and familiarize yourself with
engineering notation for all other numbers. Some common engineering
prefixes are shown in the table below.
Electric Charge
You know that an atom, in its neutral state, has a charge of zero.
You also know that if a neutral atom gains an electron, it becomes an
ion with a charge of 1-. This definition of charge works fine when
talking about one atom, but when working with large numbers of atoms, a
more practical definition of charge is needed, i.e. electric charge.
The unit for electric charge (denoted by the letter ‘q’) is the Coulomb
(C). When measured in Coulombs, an electron has a charge of
approximately -1.60 × 10
−19 C. A proton, then, would have a charge of +1.60 × 10
−19 C.
Example: Find the charge of 5.1×10
18 ions of copper (Cu). Each copper ion has a charge of 2+.
Solution: The copper ions have a surplus of protons, which
means that the copper will have a positive charge. Multiply the
fundamental charge of each ion times the number of ions. This gives the
number of extra protons. Now multiply the number of extra protons by
the charge, in Coulombs, of a proton.
q = 2 x 5.1 x x 1.60x = 1.63 C
Coulomb’s Law
Coulomb’s law defines the magnitude of the force between two charges as:
where q
1 and q
2 are the two charges in
Coulombs, r is the distance between the two points in meters, and the
permittivity constant of free space is equal to 8.85 × 10
−12
F/m (Farads/meter). If the force is negative, the two charges attract
each other while a positive force means the two charges repel each
other. The constant
is known as the electrostatic constant Kc, where
Note: Newtons (N) are a unit of force.
If you’ve ever experimented with magnets, then you have witnessed
this law before. Two magnets repel and attract each other depending on
the orientation of their poles. This equation also shows that the force
between two charges grows exponentially as they move together because
of the r
2 in the denominator. You may have noticed this
phenomenon as well. Two magnets attract or repel each other when placed
very close together, but the force between them dies off rather quickly
as they’re pulled apart.
Electric Current
Current is the flow of charge per unit time and is measured in amperes (A). Current is represented by the letter ‘I’.
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As the formula above indicates, one amp of current is equal to the
flow of one Coulomb of charge per one second. In other words, a wire
carrying one amp of current moves one Coulomb of charge through the wire
every second. When you are working with electricity, keep in mind that
one amp is a large amount of current; less than 100 mA of current can
kill you!
Voltage
Voltage is the difference in electric potential between two points
and is measured in Volts (V). If you’ve taken physics, electric
potential is similar to the concept of potential energy, except in this
instance, electric potential is equal to the potential energy per unit
charge. Voltage can be seen as the electric pressure, or driving force,
that causes current to flow. You may also see voltage referred to as
electromotive force.
An important concept to understand when working with voltage and
current is that there can be voltage without current flow, but there
cannot be current flow without a voltage. For example, think of two
people on opposite sides of a box. If both of them apply the same
amount of force, the cart will not move. However, if one of them
applies more force, the box will move. In both instances, a force
(voltage) was applied to the cart (electrons), but only when there was a
difference in force did we witness the cart move (current).
Conventional Current Flow
In the example above, the cart moves away from the person applying
more force toward the person applying less force. Current and voltage
interact in a similar manner in that current flows from higher voltages
to lower voltages. In other words, current is said to flow from the
positive terminal of a battery to the negative terminal. This is
because current is described as the flow of positive charges. The
electrons that actually carry the charge through the wire have a
negative charge. Therefore, by definition, current flows in the
opposite direction of the flow of electrons.
Water Analogies
The challenge of learning the concepts of electricity is that
electrons are hard to see and it’s hard for people to tell what is going
on in a circuit. Analogies to water have been made to help people
understand different concepts encountered in electrical engineering.
Current, as you might have guessed, is compared to the flow of water
while voltage is the difference in water pressure between two points.
More water analogies will be made throughout the course to help you
understand new concepts.
This water analogy provides another example of how there can be
voltage, but no current. Think of the build up of pressure behind a
dam. The dam pushes back on the water, allowing no water to flow. This
situation is similar to a battery. An ideal 12 V battery always has a
potential difference between its terminals of 12 V, but no current flows
until the battery is connected to a circuit.
Final Remark
Current is a through variable and voltage is an across variable.
Current flows through circuits, voltage does not. Rather, voltage is
the
potential for current to flow. When referring to voltage,
never say “the voltage through the resistor.” Instead, say “the voltage
across the resistor” or “the voltage at a node.” This article was
written and edited by Ryan Eatinger, Kansas State University
(reatinge@ksu.edu), thanks for the donation.