December 1942 Radio-Craft
Wax nostalgic about and learn from the history of early electronics.
See articles from Radio-Craft,
published 1929 - 1953. All copyrights are hereby acknowledged.
When civil engineers and mechanical engineers take their introductory
classes in hydraulics, are the taught that the functional equivalent
of water pressure in a pipe is equivalent to voltage in a battery,
and that the rate of water flow is equivalent to current in a circuit,
and that the diameter and surface finish of pipes are equivalent
to resistance in electricity... in the same manner that electronics
students are taught from the opposite point of view? The answer
is 'yes,' they are. It's kind of funny how for some reason using
an analogy from another familiar physical process always seems to
help make more sense of the subject at hand. In fact, for macro
level problems, the mathematical equations that govern mechanical
and electrical systems are identical, with only the objects and
units being different. Oscillating LC (inductor and capacitor) tank
and damping circuits have equations that look just like spring and
dashpot systems that perform analogous mechanical functions - both
in the time domain and the frequency domain. It is not until you
get into really specific components and functions that unique equations
emerge for electrical and mechanical studies. This article that
appeared in a 1942 edition of Radio-Craft illustrates how
the basics have not changed in over half a century.
By Willard Moody*
Fig. 1 - Voltage / water pressure analogy.
Most of our readers are already familiar with the helpful and
instructive explanations of electrical theory which Mr. Moody has
given us from time to time. In these days when thousands of school
boys and young men are studying radio before entering the armed
forces, they must cram in a month or two what usually takes a year
to learn. So to these young men we say that Mr. Moody's articles
will be found of tremendous interest and assistance. .
Th volt is the unit of electromotive force or potential difference,
which will send a current of 1 ampere through a resistance of 1
ohm. A standard battery in the Bureau of Standards has a terminal
voltage or potential difference of 1 volt, when constructed according
to certain specifications. In radio work, sensitivity of a receiver
may be stated in microvolts. A microvolt is a volt divided by the
number 1,000,000, or 10 raised to the minus six power. Sensitivity
is also stated, occasionally, in millivolts per meter. A millivolt
is a volt divided by 1,000.
Voltage may conveniently be considered as pressure. The idea
of a water tower filled with water and exerting pressure upon the
surface of a pipe connecting to the tower is a simple analogy or
explanation, Fig. 1.
A storage battery or dry cell may be considered a reservoir of
electrical energy from which current is drawn when the pipe connecting
to the battery is not plugged up. If a plug in the form of resistance
is inserted in the pipe, there will be opposition to the flow of
current and only a thin stream will leak through. Electrical leakage
is very similar. The positive terminal of the battery of electrical
generator may be thought of as the point where the pipe connects
to the tank and the pressure exerted on the pipe at this point will
be the potential force or voltage.
The current in an electric circuit is rated in amperes or fractional
parts of the ampere. In radio work a meter may have a movement,
or full scale reading of 1 milliampere.
A milliampere is an ampere, divided by 1,000, or expressed decimally
is 0.001 ampere. An ampere is the current that flows in a circuit
having a resistance of 1 ohm and a voltage or potential difference
of 1 volt.
In certain instruments, the sensitivity or full scale reading
may be 50 micro-amperes. A micro-ampere is an ampere divided by
Current may be thought of as a flow of electrons through a wire
similar to a flow of water in a pipe. A heavy current (or large
number of amperes) is like a flow of several gallons of water per
second. A light current would have a small number of amperes. In
radio, a small current would be measured in micro-amperes. An ordinary
house fuse has a rating of ten or fifteen amperes in the branch
circuit, and may be 25 amperes in the wattmeter circuit. A radio
of average console size might draw 1-1/2 amperes from the 115 volt
power line. A 150 watt bulb would draw about the same current in
amperes on the same line.
Resistance is stated in ohms. An ohm is the unit of opposition
offered to the flow of electric current, and in the Bureau of Standards
is the resistance of a piece of special wire under certain conditions
of temperature. One ohm will be equal to 1 volt divided by 1 ampere.
That is Ohm's Law and was discovered by a scientist named Simon
Ohm in whose honor the unit is named. Ohm's Law is so fundamental
and is used so often in radio and electrical work that it must be
Ohm's Law states that current flowing in a circuit is equal to
the voltage across the circuit, divided by the resistance of the
circuit, or expressed in symbols:
I = E / R
This relation holds true only when I is in amperes, E is in volts,
and R is in ohms. If a current was measured in milliamperes (or
thousandths of an ampere), it would have to be changed to amperes
by being expressed as a decimal part of an ampere, before being
used in the Ohm's Law formula.
Suppose R were in megohms (mega, million, plus ohms). It would
not have to be changed to be used in the formula, because it is
already in ohms.
The electrical power in a circuit is rated in watts. One horsepower
is equivalent to 746 watts. In amateur radio transmitters the plate
power to the final stage is legally limited to 1,000 watts or 1
kilowatt. A large broadcasting station, on the other hand, may have
a power of 50,000 watts or 50 kw.
Fig. 2 - Impedance triangles
An ordinary console radio may have a power rating of 150 watts:
but the circuit resistors used in that radio are rated 1 watt or
1/2 watt. An electric soldering iron might have a rating of 100
watts; and an electric clock might draw no more than 1/2 watt.
The watt in a direct current circuit is equal to the product
of voltage and current, or expressed as a formula:
W = I x E
The watt is the unit of electrical energy or work, hence the
symbol "W." Lately, however, the symbol "P" has enjoyed wide usage
and also represents wattage or power. The capacity of a water tank
represents the electrical power in a water analogy. The wattage
dissipation of a resistance will be the power lost as the result
of heating the resistance, which is work done. An electric lamp,
when heated, radiates both heat and light. That is, the conversion
of electrical power into other useful form of energy. A radio loudspeaker
will convert electrical power into mechanical power, and this in
turn will set up a pressure in the air which reacts on our ear drums.
The pressure on the ear drum is then converted into an electrical
current in the nerve and transmitted to the brain, where we receive
consciousness of the sound heard.
An electric motor, when fed electrical power, turns its shaft
and does work. Conversely, an automobile generator has its shaft
turned by engine, and is thus supplied mechanical power, which it
converts or changes into electrical power that is used to charge
up the storage battery in the car's ignition system.
The power is an alternating current circuit will be equal to
the product of three factors, that is, voltage, current, and a third
factor called the "power factor."
The power factor of a circuit is the percentage of resistance in
the circuit. A lamp bulb, being all resistance practically, has
unity power factor; this is expressed as 1. The voltage times the
current times 1 will be the power. If the power factor is something
less than 1, it will be expressed as a percentage, say 90%, which
is shown as .9 and is used to multiply the voltage and current.
An ordinary A.C. voltmeter or ammeter, such as used in radio
servicing or electrical power work, will read in what are termed
effective values. The effective value of an alternating current
produces the same heat in a one-ohm resistance, as the heat that
is produced by a direct current. If the direct current voltage were
1 volt and the resistance were 1 ohm, the current would be 1 ampere.
If an effective alternating current volt were supplied to a resistance
of 1 ohm, the effective current would be 1 ampere and the heat produced
in the 1 ohm resistance would be the same as with the direct current.
The power would also be the same and the power factor would be 1,
The power factor in an alternating current circuit takes into
account a quantity called impedance. The symbol "Z" is used to represent
impedance and this quantity is stated in ohms. The ratio of R to
Z is called the power factor. That is, R divided by Z equals the
power factor. In a parallel circuit of inductance and capacity,
at resonance, the impedance is minimum and is a pure resistance.
This is so because the reactances of the circuit have cancelled
out and only the resistance of the coil is left. All these new terms
will be explained fully as we go on, Fig. 3.
The power factor is also equal to the cosine of the phase angle,
or, cos θ (theta) equals R divided by Z.
Phase Angle and Reactance
Fig. 3 - Series inductance, capacitance & resistance
Fig. 4 - Resonant frequency
Fig. 5 - Resistive circuit current & voltage "in
In a direct-current circuit, when the battery is connected to
a resistance, the current immediately climbs to its peak or maximum
value and remains there so long as the battery is connected. The
action is instantaneous or occurs at once, Fig. 5.
In an alternating-current circuit, when voltage is applied to
a coil, the current does not immediately flow into the coil because
there is a magnetic field about the turns of wire in that coil,
which creates a back electromotive-force that is opposite in direction
to the applied electromotive force or voltage. As a result, there
is a time-lag between current and voltage, and the voltage in a
coil circuit leads the current by 90 degrees. This effect is called
reactance and is measured in ohms, just as impedance and resistance
are measured in ohms. The inductive reactance limits the current
flow in an alternating current circuit. The current I will be equal
to E divided by X. The symbol for reactance is X, Fig. 2.
It is obvious that the effect of the inductance of the coil,
is to limit the current. This limiting will increase as the frequency
of the alternating current is increased. The equation for inductive
XL = 2πfL
where "L" is the inductance in henrys, "f" is frequency in cycles
and "XL" is the inductive reactance in ohms.
Capacitance and Reactance
As the reactance of the coil increases with frequency or an increase
in the inductance, the reactance is said to be a positive quantity.
A condenser or capacitor, on the other hand, has a negative characteristic,
Its reactance varies inversely or negatively as the capacity or
frequency is raised. The equation for capacity reactance is:
where "XC" is in ohms, "C" in farads, "f" in cycles.
When voltage is applied to a condenser, current flows into the
plates of the condenser. But before there can be a potential difference
between the condenser plates, or before those plates can acquire
or get a charge of electricity, current must flow into the plates.
Thus, the current gets there first and the current is said to lead
the voltage by 90 electrical degrees. The voltage is said to lag
the current (which is just the opposite of what holds true in the
case of the coil).
In a direct current circuit voltage and current reach their peaks
(or maximum values) at the same instant.
In an alternating-current circuit the voltage and current reach
their peak values at the same instant only when the circuit is composed
of pure resistance and has no reactance. Under that condition the
power factor, or ratio R/Z, is said to be unity, and the circuit
is termed "resistive." If the power factor is less than 1, the circuit
is partially "reactive."
An example of such a condition occurs in parallel resonant circuits
(that is, tuning circuits), where, when the condenser (or the inductance
in some cases) is tuned, the reactance of the condenser equals the
reactance of the inductance. Being equal there is no effect on the
phase relationship, so the resistance limiting current flow consists
of the resistance of the wire in the inductance and in the leads.
This resistance has no effect on the phase angle. The so-called
peak of the resonant frequency is attained under these conditions.
(See Fig. 4.)
The diagram shown, consisting of L, R and C is the equivalent
circuit of the inductance, with its d.c-resistance R; and the condenser
C. Land C of course are in terms of ohms to make this equivalent
The formulae given show the relationships existing; and the resonant
frequency diagram shows peak or resonant frequency between two side-band
frequencies f-1, and f-2.
It is important to remember that power is never lost in a pure
reactance. Power is lost only in resistance. Reactance stores energy,
and it is the reactance of a coil or condenser that makes the coil
or condenser act as an electrical storage tank. In a parallel circuit,
at resonance, when coil reactance equals condenser reactance, there
is a cycle of energy being poured from coil to condenser and vice
versa. It's like having two glasses, one filled with water and the
other empty. You take the water in one glass and pour it into the
other, then back again. You can repeat this indefinitely. If you
spill some of the water, that is power lost. Your clumsiness represents
resistance. If you are very clumsy, you are very resistive and lose
power readily. A coil having a high resistance would lose power
constantly in the circuit, until all of the available power was
used up. The same applies to a condenser. In any case, the more
efficient is the coil or condenser, the less is the power factor.
The energy being poured back and forth represents reactive or circulating
current. It is phantom or unreal power although the current is there
and is very real. The wires or conductors in an alternating current
system, such as the wiring in a factory, must carry reactive current
if the power factor of the line is not close to 100%. Synchronous
motors are sometimes switched into such circuits, because they draw
a reactive current which balances the system and restores the power
Posted September 21, 2014