How voltage, current, and resistance relate
An electric circuit is formed when a conductive path is created to allow free electrons to continuously move. This continuous movement of free electrons through the conductors of a circuit is called a current, and it is often referred to in terms of “flow,” just like the flow of a liquid through a hollow pipe.
The force motivating electrons to
“flow” in a circuit is called voltage. Voltage is a specific measure of
potential energy that is always relative between two points. When we
speak of a certain amount of voltage being present in a circuit, we are
referring to the measurement of how much potential energy exists to move electrons from one particular point in that circuit to another particular point. Without reference to two particular points, the term “voltage” has no meaning.
Free
electrons tend to move through conductors with some degree of friction,
or opposition to motion. This opposition to motion is more properly
called resistance. The amount of current in a circuit depends
on the amount of voltage available to motivate the electrons, and also
the amount of resistance in the circuit to oppose electron flow. Just
like voltage, resistance is a quantity relative between two points.
For
this reason, the quantities of voltage and resistance are often stated
as being “between” or “across” two points in a circuit.
To be able
to make meaningful statements about these quantities in circuits, we
need to be able to describe their quantities in the same way that we
might quantify mass, temperature, volume, length, or any other kind of
physical quantity. For mass we might use the units of “kilogram” or
“gram.” For temperature we might use degrees Fahrenheit or degrees
Celsius.
| Quantity | Symbol | Units of Measurement | Unit Abbreviation |
| Current | I | Ampere ‘Amp’ | A |
| Voltage | E or V | Volt | V |
| Resistance | R | Ohm | Ω |
The “symbol” given for each quantity is the standard alphabetical
letter used to represent that quantity in an algebraic equation.
Standardized letters like these are common in the disciplines of physics
and engineering, and are internationally recognized. The “unit
abbreviation” for each quantity represents the alphabetical symbol used
as a shorthand notation for its particular unit of measurement. And,
yes, that strange-looking “horseshoe” symbol is the capital Greek letter
Ω, just a character in a foreign alphabet.
Each unit of measurement is named after a famous experimenter in electricity: The amp after the Frenchman Andre M. Ampere, the volt after the Italian Alessandro Volta, and the ohm after the German Georg Simon Ohm.
The
mathematical symbol for each quantity is meaningful as well. The “R”
for resistance and the “V” for voltage are both self-explanatory,
whereas “I” for current seems a bit weird. The “I” is thought to have
been meant to represent “Intensity” (of electron flow), and the other
symbol for voltage, “E,” stands for “Electromotive force.” From what
research I’ve been able to do, there seems to be some dispute over the
meaning of “I.” The symbols “E” and “V” are interchangeable for the most
part, although some texts reserve “E” to represent voltage across a
source (such as a battery or generator) and “V” to represent voltage
across anything else.
All of these symbols are expressed using
capital letters, except in cases where a quantity (especially voltage or
current) is described in terms of a brief period of time (called an
“instantaneous” value). For example, the voltage of a battery, which is
stable over a long period of time, will be symbolized with a capital
letter “E,” while the voltage peak of a lightning strike at the very
instant it hits a power line would most likely be symbolized with a
lower-case letter “e” (or lower-case “v”) to designate that value as
being at a single moment in time. This same lower-case convention holds
true for current as well, the lower-case letter “i” representing current
at some instant in time. Most direct-current (DC) measurements,
however, being stable over time, will be symbolized with capital
letters.
One foundational unit of electrical measurement, often
taught in the beginnings of electronics courses but used infrequently
afterwards, is the unit of the coulomb, which is a measure of
electric charge proportional to the number of electrons in an imbalanced
state. One coulomb of charge is equal to 6,250,000,000,000,000,000
electrons. The symbol for electric charge quantity is the capital letter
“Q,” with the unit of coulombs abbreviated by the capital letter “C.”
It so happens that the unit for electron flow, the amp, is equal to 1
coulomb of electrons passing by a given point in a circuit in 1 second
of time. Cast in these terms, current is the rate of electric charge motion through a conductor.
As stated before, voltage is the measure of potential energy per unit charge
available to motivate electrons from one point to another. Before we
can precisely define what a “volt” is, we must understand how to measure
this quantity we call “potential energy.” The general metric unit for
energy of any kind is the joule, equal to the amount of work
performed by a force of 1 newton exerted through a motion of 1 meter (in
the same direction). In British units, this is slightly less than 3/4
pound of force exerted over a distance of 1 foot. Put in common terms,
it takes about 1 joule of energy to lift a 3/4 pound weight 1 foot off
the ground, or to drag something a distance of 1 foot using a parallel
pulling force of 3/4 pound. Defined in these scientific terms, 1 volt is
equal to 1 joule of electric potential energy per (divided by) 1
coulomb of charge. Thus, a 9 volt battery releases 9 joules of energy
for every coulomb of electrons moved through a circuit.
These
units and symbols for electrical quantities will become very important
to know as we begin to explore the relationships between them in
circuits. The first, and perhaps most important, relationship between
current, voltage, and resistance is called Ohm’s Law, discovered by
Georg Simon Ohm and published in his 1827 paper, The Galvanic Circuit Investigated Mathematically.
Ohm’s principal discovery was that the amount of electric current
through a metal conductor in a circuit is directly proportional to the
voltage impressed across it, for any given temperature. Ohm expressed
his discovery in the form of a simple equation, describing how voltage,
current, and resistance interrelate:
In this algebraic expression, voltage (E) is equal to current (I)
multiplied by resistance (R). Using algebra techniques, we can
manipulate this equation into two variations, solving for I and for R,
respectively:
In this first example, we will calculate the amount of current (I) in a circuit, given values of voltage (E) and resistance (R):
If you know E and I, and wish to determine R, just eliminate R from the picture and see what’s left:
Lastly, if you know I and R, and wish to determine E, eliminate E and see what’s left:
Eventually, you’ll have to be familiar with algebra to seriously study
electricity and electronics, but this tip can make your first
calculations a little easier to remember. If you are comfortable with
algebra, all you need to do is commit E=IR to memory and derive the
other two formulae from that when you need them!
REVIEW:
- Voltage measured in volts, symbolized by the letters “E” or “V”.
- Current measured in amps, symbolized by the letter “I”.
- Resistance measured in ohms, symbolized by the letter “R”.
- Ohm’s Law: E = IR ; I = E/R ; R = E/I
