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 "pound" or "gram." For temperature we might use degrees
Fahrenheit or degrees Celsius. Here are the standard units
of measurement for electrical current, voltage, and
resistance:
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 (apologies to any Greek readers here).
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:
Let's see how these equations might work to
help us analyze simple circuits:
In the above circuit, there is only one
source of voltage (the battery, on the left) and only one
source of resistance to current (the lamp, on the right).
This makes it very easy to apply Ohm's Law. If we know the
values of any two of the three quantities (voltage, current,
and resistance) in this circuit, we can use Ohm's Law to
determine the third.
In this first example, we will calculate the
amount of current (I) in a circuit, given values of voltage
(E) and resistance (R):
What is the amount of current (I) in this
circuit?
In this second example, we will calculate
the amount of resistance (R) in a circuit, given values of
voltage (E) and current (I):
What is the amount of resistance (R) offered
by the lamp?
In the last example, we will calculate the
amount of voltage supplied by a battery, given values of
current (I) and resistance (R):
What is the amount of voltage provided by
the battery?
Ohm's Law is a very simple and useful tool
for analyzing electric circuits. It is used so often in the
study of electricity and electronics that it needs to be
committed to memory by the serious student. For those who
are not yet comfortable with algebra, there's a trick to
remembering how to solve for any one quantity, given the
other two. First, arrange the letters E, I, and R in a
triangle like this:
If you know E and I, and wish to determine
R, just eliminate R from the picture and see what's left:
If you know E and R, and wish to determine
I, eliminate I 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!
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REVIEW:
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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".
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Ohm's Law: E = IR ; I = E/R ; R = E/I
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