In 1827, a German
physicist and mathematician published a scientific paper in which he
put forth the principle that voltage, current and resistance in an
electrical circuit were interrelated. When the value of one changed,
he said, the others would change, and in a predictable way.
Georg Simon Ohm
The paper included a
formula that described those interactions. The equation is
fundamental to the understanding of the way electrical circuits work.
The physicist was Georg Ohm, and his seminal formula is known all
over the world.
Ohm's Law says that
when resistance in a circuit is unchanged, voltage varies in direct
proportion to current. The formula is written as E=IR. This
simple mathematical statement was an amazing addition to the
knowledge of electronics and is one that engineers learn at the
beginning of their careers.
More importantly, it
led to a whole slew of electrical “laws” and formulas that,
together, determine how every piece of equipment broadcasters use is
designed and operates.
LIGHTNING IN A BOTTLE
Ohm worked out his law
when the knowledge of electrical force itself was not yet 100 years
old. The Greeks knew and wrote about “static” electricity a few
thousand years before Ohm and even named the electron, which means
“amber” in Greek, a common source of static electricity; but it
was not until the 1700s that experimenters began to work out the
properties of electrical force.
As we learned in grade
school, Benjamin Franklin speculated that lightning might in fact be
electricity and wrote extensively about the subject in the early part
of the 18th century. But it was not until 1752 that he got up enough
courage to hoist his kite into a thunderstorm to prove it, by
capturing the electrical discharge from a nearby strike in a glass
The bottle was called a
Leyden Jar, named by one of its inventors, Pieter van Musschenbroek,
in honor of his hometown of Lieden, Germany. Franklin’s experiment,
fortuitously performed with a Leyden Jar rather than something that
might have been called a Musschenbroek Bottle, is the origin of the
saying that having a great idea is like having “lightning in a
Ohm and others like
him, lacking Franklin's sense of adventure, waited for a more
controllable and less deadly source of electricity, and were rewarded
by the experiments of two Italian scientists: Luigi Galvani and
Alessandro Volta (the latter being the namesake of the unit of
electric potential; the “volt” in Ohm’s formula).
These men found that
stacking alternating sheets of copper and zinc between an acidic
solution created a sustainable electrical force. Originally these
were called the Galvanic cell and the Voltaic pile. The names of the
two devices, sounding a bit sinister perhaps, soon changed to
As Ohm knew, a wire
connected between the two different plates of one of Volta’s
batteries would cause current to flow. He also found that increasing
the length of the wire decreased the current. He had discovered
electrical resistance. The exact relationship between voltage current
and resistance was not understood and that is what Ohm worked out.
By the time he got
around to it, though, Volta’s name had already been tapped as the
unit of EMF, or Electromotive Force, another name for electrical
potential. That is why voltage is abbreviated with an “E” in
The unit for current
was similarly named for Andre-Marie Ampere, a French scientist, so
that only left resistance for Ohm, and that is what he got. The “Ohm”
is the standard unit of electrical resistance, and is technically
defined as the result obtained when one volt of electrical force
causes one ampere of current to flow in a circuit.
Much later Ohm was
honored again when the people who name these things (who are those
guys?) gathered together to assign an appropriate Nom de Plume
to the unit of electrical conductance. It being the exact reverse of
resistance, they named it that: The Mho. Must have been Opposite Day.
KEEPING IT SIMPLE
The most elegant
aspect of Ohm’s Law is its simplicity. If two of the variable
quantities are known, the formula can be used to find the third. I
learned the law using a simple circle graphic.
By covering up the
unknown parameter, you can immediately see how to use the other two
to find the missing one. Covering the voltage term E leaves IR
on the bottom of the circle. The value for E is found by
multiplying those two variables.
If a circuit has three
amperes of current I flowing through 300 ohms of resistance R,
the applied voltage E equals 3 x 300, or 900 volts. Using the
same numbers, if the voltage and current are known, covering up I
leaves E over R. Dividing E of 900 volts by R of
300 ohms gives the answer of I=3 amperes. And you don’t
have to be smarter than a fifth grader.
Ohm's Law led to a
derivative, which substitutes P for power in the top half of
the circle and replaces the R in the circle with the voltage
term E. Power is measured in watts, named for James Watt, the
Scottish inventor of the first practical steam engine.
Watt was not an
electrical engineer or scientist, but made such extensive
calculations of power — and in the process coined the term
“horsepower” — that the unit of electrical power was named
after him, again by those mysterious guys who do that sort of thing.
In any event, the formula in that iteration works exactly the same as
IN PRACTICE IT’S
Both formulas are
practical in ways that might not be immediately apparent and can be
used to diagnose many problems that broadcast engineers routinely run
into. For example, why does a power supply blow a fuse?
If we can assume that
the power company has not inadvertently throttled up the grid and
sent your studio 220 volts instead of the normal 110, then according
to Ohm’s Law, there can be only one reason: The internal resistance
of the power supply or its associated circuits has gone down, because
the law tells us that when resistance goes down, current goes up.
It follows that if the
resistance goes low enough, the current will go high enough to blow
the fuse. And here’s the thing: it doesn’t even have to be a dead
short (meaning no resistance at all).Ohm’s Law can tell you precisely how low the resistance
has to go before the current flow will exceed the rating of the fuse.
when something needs fixing fast.
Using the power
variation of the formula can help diagnose transmitter problems, or
just to confirm normal operation. If you know your transmitter’s
operating efficiency (either tube-type or solid-state) and the output
power is 5,000 watts, you can figure out how much current should be
coming from the power supply, provided you know the supply voltage.
If the supply voltage
is 50 volts (not uncommon in a solid-state transmitter) and the
transmitter efficiency is 90 percent, the power supply current has to
be 111 amps, if all is well. The calculation is 5,555 watts (the
power needed for the transmitter to make 5,000 watts of RF assuming
90 percent efficiency), divided by 50 volts, which equals 111 amps.
If the power supply
current meter is reading significantly higher or lower than that,
something is wrong.
Similarly, in a
tube-type transmitter, if a current overload relay intermittently
trips, Ohm’s Law tells us that the resistance of the circuit being
protected by the relay has decreased, or the supply voltage has
increased. According to Ohm’s Law, when current increases there can
only be one of two reasons: Either the voltage has increased
(entirely possible in a transmitter circuit) or the internal
resistance has decreased.
Knowing the formula
makes all the difference in diagnosing and finding the problem.
Georg Ohm died in
1854, 48 years before Marconi astounded the world by broadcasting a
signal across the Atlantic and setting the stage for the future of
radio. But Marconi and all who have followed him would have gotten
nowhere without Ohm’s Law. It’s the true Formula One.
Jim Withers is owner
of KYRK(FM) in Corpus Christi, Texas, and a longtime RW contributor.
He has four decades of broadcast engineering experience at radio and
television stations around the country.