by
R. W. Stuart
E=IR - I=E/R - R=E/I
~~A Basic Electricity, Part 01~~
I intend to start a series dealing with simple electricity as it
applies to our RC activity. 60 years of working with electricity has convinced
me of one thing: electricity will do precisely and only what it is programmed
to do by the forces of the universe, and there is nothing you can do about
this
other than understand the few basic properties of electricity. Once the
properties are understood you can arrange your schemes and machines to
accommodate the electricity you cannot change electricity!
All materials are composed of atoms which are protons surrounded by a
swarm of electrons. Copper, a good conductor of electricity, has an outer
shell
of electrons which can easily migrate through the protons and it is the motion
of the electrons which manifests itself as electricity. Gold, silver, lead,
aluminum and other metals are generally good conductors. Other materials, such
as glass (an insulator), have tightly bound electrons and are poor conductors.
Carbon is near to being right in the middle as a conductor and thus the term
semiconductor.
When electrons flow in a conductor it is called current and is
expressed in amperes. An ampere is defined as so many trillions of electrons
moving past a point every second. The cap I is the symbol used for current
and may be amps, miliamps (ma), or microamps (mu a). The two varieties of
current are direct current (DC) and alternating current (AC). Batteries are DC
and your house jacks are AC. AC is the preferred form of electricity for
transmission, in spite of Edison’s stubborn insistence on DC. Part of Pa. and
NJ are still on DC.
In order to get electrons to flow in a conductor a force must be
applied to drive the electrons. This force is called the electromotive force
(emf) and is expressed as volts with the symbol E. Your flight batteries are
nom. 4.8 VDC.
If a force is required to move electrons through a conductor, then the
conductor is presenting some resistance to the flow of electrons and this
resistance is expressed as ohms with the symbol R. Your transmitter has a
resistance of 200 ohms or so.
The first and only relation between I, E, and R is a thing called ohms
law and is the fundamental proposition for all of electricity- all other
concepts are just variations of ohms law. The law states that in a circuit the
voltage is equal to the current times the resistance or E=IR, (volts equals
amps times ohms). All forms of ohms law, merely algebraic manipulations, are:
E=IR, I=E/R, and R=E/I. If you have 6 volts and 2 amps in a circuit, the
resistance must be 3 ohms (E=IR or 6=2x3). That’s it and we will play more
with
this stuff in the future.
Note: Volts after pioneer Volta, amps after Ampere, and ohms after
Ohmes; all great early scientific thinkers.
Keep copies of this stuff for review and reference- start a file for
them. It might be worth while.
~~A Basic Electricity, Part 02~~
The relationship between voltage, current and resistance in any
circuit
has not changed since the Part 01 note on electricity which is a good thing,
since nothing could be more straightforward, simple, and precise than E=IR.
Another principle of electricity states that the action (formation of heat,
light, force, noise, etc.) occurs where the voltage drop, IR, occurs. Also,
the
sum of the voltage drops around a series circuit is always equal to the
source voltage; E1+E2+E3.....=IR1+IR2+IR3+IR4...... The most useable form of
ohms law is E=IR because it teaches you to think in terms of voltage drops.
For your airborne system, battery voltage ( E ) is equal to the IR (
wire drop ) + IR ( receiver drop ) + IR ( ail servo motor drop ) +
others......Wire drops show up as heat and may be only microvolts where servo
drops show up as mechanical motion and may be full voltage ( battery )
drops as
well as some heat and a little voltage drop to operate the servo logic
circuit.
Note that the ail servo drop and the ele servo drop are not added together-
they are parallel circuits, explained in the next paragraph. So, the
servos
suck up a lot of the available energy and stiff control surface hinges add
severe loading to the servos.
The two types of circuits are either series or parallel circuits. A
flashlight is a series circuit: starting with the battery positive terminal,
then the on-off switch, then the bulb, and finally back to the battery
negative
terminal. All of the parts are connected with wires (conductors) and the same
current flows through each part. E ( batt ) = IR ( wire ) + IR ( switch ) + IR
( bulb ) +IR ( batt ). Yes, batteries have an internal resistance which makes
them hot when heavily loaded like a dead short, right John? With the switch
closed ( bulb on ) we have a circuit which follows ohms law. If the switch is
opened we have no light from the bulb (off). Do we still have a circuit? Does
E=IR still pertain? Yes and yes. The air gap between the open switch blades
may
have a resistance higher than 300,000,000 ohms ( 300 megohm ) and that gap
must
drop- if ohms law is universal- the 3 volt battery voltage. I=E/R at the open
switch numerically is l ( current ) = 3/300,000,000 or one millionth of an
ampere ( microamp ). This is not enough current to light the bulb, not enough
to heat the air at the switch, and not enough to run the battery down any more
than its normal shelf loss. The switch does its job and the circuit, now
functionally open, still validates E=IR.
Most of the normal house wiring jacks ( wall sockets ) provide
parallel
circuits to the toaster, vac, TV and other household devices. Each device
plugged into the wall is in parallel with each other plugged in device and the
typical modern house may have thirty things plugged in at one time— thirty
parallel circuits. 3 cheers for CEI and Edison! Each device looks directly at
the source voltage and in a properly engineered system has no electrical
knowledge about the other connected loads.
Complex circuits may be a confusing mixture of parallel and series
circuits, but both parallel and series circuits may be simplified as the
circuitry is analyzed. The process involves some rather messy math, but we
will
work with rather simple parallel-series circuits. The four or so RC servo
motors in an airborne system are connected in parallel with the flight
battery,
but controlled by the servo logic.
~~A Basic Electricity, Part 03~~
Series circuits may be solved by substituting the sum of the
resistances with a single equivalent resistance and applying E=IR. Using a
12 v
batt, 1 ohm, 2 ohm & 3 ohm resistors in a series circuit, what is the circuit
current? I=E/R or I (amps) = 12 volts/ ( 1 + 2 + 3 ) ohms = 12/6 = 2 amp. Note
that in a series circuit, the same current passes through each resistor and
the
1 ohm resistor drops 2 volts (IR= 2x1), the 2 ohm resistor drops 4 volts (
IR =
2x2), while the 3 ohm resistor drops 6 volts (IR = 2x3). And, sure enough,
the
sum of the drops is equal to the source voltage. 12 = 2 + 4 + 6.
Parallel circuits may be solved by substituting the reciprocal (don’t
panic) sum of the resistors in parallel which becomes a series circuit with
only one resistor as the reciprocal sum is applied. The reciprocal of a
number,
N, is 1/N and the reciprocal of 7 is 1/7. We will make a parallel circuit:
a 12
volt batt is connected directly across a 6 ohm resistor and a 12 ohm resistor
at the same time. Both resistors are looking directly at 12 v so the voltage
drop across each resistor is the same- 12 v. The current in the 6 ohm resistor
is I=E/R = 12/6 = 2 amp, the current in the 12 ohm resistor is I=E/R = 12/12 =
1 amp. The total current in the circuit is 3 amp and now R=E/I = 12/3 = 4
ohms,
so a single 4 ohm resistor may be substituted for the 6 & 12 ohms in parallel.
This verifies the reciprocal approach to parallel circuits.
1/RS = 1/R1 + 1/R2 + 1/R3.....where R1, R2, R3..... are parallel
resistors and RS is the equivalent single resistor which may be substituted
for
the simplification of the circuit. In the 6 & 12 ohm circuit above, 1/RS = 1/6
+ 1/12 = 2/12 + 1/12 = 3/12 or 1/4. If 1/RS = 1/4, then multiply both sides of
the equation by RS, whereby RS/RS = RS/4. RS/RS is 1 so 1 = RS/4, and
multiplying both sides of the equation by 4, the equation now becomes 4x1 = RS
or RS = 4 ohms. The very basic math should help. We all need a little of that
once in a while.
When working with very complex circuits, the process is exactly the
same. A circuit may be composed of a parallel circuit part of which
may
be series with parallel internal branches- many of them- and the solution
requires some nasty math. Most simple circuits may be solved easily by keeping
in mind that series resistances are additive and parallel resistances are
additive by their reciprocals. Then the application of the ohm relationship
becomes automatic and intuitive. In a series circuit the same current flows
through each resistor and the addition of more resistors can only lower the
circuit current. In a parallel circuit each resistor is looking at the same
voltage and the addition of more resistors can only increase the circuit
current. Think in terms of voltage drop, IR, and you will become proficient
with circuits and the mystery disappears.
Resistors may be made of wire, carbon-clay mixtures and most other
materials. They are color coded and have power ratings from 1/8 watt to many
thousands of watts, in values from 0.1 ohm to hundreds of megohms, and
accuracies from 0.1% to + or - 20%. Precision resistors are used in meter
circuits and are very expensive. Your skin resistance is nominally 30,000
ohms,
which is why you cannot feel the 4.8v flight batt voltage ( your
sensitivity to
voltage may be increased a thousand fold by tasting the batt which means
your
tongue has a resistance of about 1000 ohms- however, use a meter to avoid
trauma and save your fillings).
~~Basic Electricity, Part 04~~
If two sheets of metallic foil are separated by a thin insulator and
properly terminated, they become a capacitor. The capacitor behaves like a
short term battery and can store an electrostatic charge. Capacity is
dimensioned in Farads ( F ) and microfarads are the most common usages along
with picofarads.
When a capacitor is being charged, the starting current into the
capacitor is very large and the starting voltage is small. As the capacitor
becomes charged the current decreases and the voltage increases. A fully
charged capacitor has near zero current flow and full voltage value.
If AC is applied to a capacitor, the current is said to lead the voltage and
this lead is continuous throughout the cycles and the angular difference is
known as phase angle. Since power is the product of voltage times current in
AC circuits, the phase angle ( voltage to current ) limits the power which
can
be delivered. In AC circuits the power is equal to the current times the
voltage times the cosine ( always less than 1 ) of the phase angle. In DC
the phase angle is 0 and the cosine of 0 is 1, which verifies that for DC
power, P=EI. For AC power,P=EICos of the phase angle.
When current flows in a wire a magnetic field is formed around the
wire
and the process is called inductance. Grab a pencil with all of your fingers
tight around the pencil. The pencil is the wire and your fingers are the
magnetic lines of force. Think of winding a coil, a great number of turns on a
cylinder, where each loop adds a bit of magnetic force and the resulting
electromagnet has noticeable force. Henries are the dimension of inductance
and
the usual values are in milihenries.
As the voltage is applied in an inductive circuit, the current
increases; but this increase is resisted because the increasing magnetic field
resents change. When the circuit is opened, the collapsing magnetic field,
still resisting change, produces a voltage which keeps the decreasing current
flowing for a while. In an inductive circuit the current lags the voltage and
the power is still EICos of the phase angle.
If a circuit is composed of both capacity and inductance, with
properly
balanced values, it becomes a tuned circuit. Tuned circuits peak at a
specific frequency and are the basis for most radio frequency ( rf ). Being a
form of AC, the rf alternately charges and discharges both the capacitor (
current leads the voltage ) and the inductor ( current lags the voltage ).
When
the leading and lagging currents have the same value the circuit is tuned.
At a
given frequency the optimum selection of the capacity and inductance
depends on
the freq. Fine tuning is accomplished with a variable capacitor and or a
variable inductor.
In DC work the resistance of a circuit is called ohms and the circuit
power is EI. In rf work the resistance of the circuit is called impeadance
(Z),
but is still dimensioned in ohms. When tuned, a circuit has very low
impedance and a high current for a given voltage, and when tuned looks like
pure resistance as far as power is concerned, because the lead and lag of the
circuit cancel each other.
Note the following for DC: E(volt) = I(amp)R(ohms) and math
manipulation allows that E=IR or I=E/R or R=E/I. Also P(power) =
E(volt)I(amp)--dimensioned in watts and math manipulation allows that P=EI or
E=P/I or I=P/E. Also, by substitution of IR for E, P=IRI.
Note the following for AC: E(volt) = I(amp)Z(impedance in ohms). Also
P(watts) = E(volts)I(amp) cosine of the phase angle. In a tuned circuit there
is no phase angle and the cosine of 0 degrees angle is 1- which means the
tuned
circuit has the most power. If P=EIcos phase angle, how can we get power
out of
AC when half the time the current is positive and half the time the current is
negative. Substituting IZ for E, we can show P=IZIcos phase angle, During the
negative part of the cycle, a negative I times a negative I is a positive
value thus positive power for negative current.
Some interesting stuff here: +1 times +1 is +1, -1 times -1 is +1, -1
times +1 is -1. Not too bad so far! The square root of +1 is +1, but some of
the math of electricity asks to use the square root of a -1 and the concept
will fry your brain. The square root of -1 never has and never will exist in
our universe, and since the math people must manipulate the monster, they
call
it an imaginary number (symbol lower case i ), and get on with the work. i
times i is -1. Strange!! We will not monkey with this stuff.
~~Basic Electricity, Part 05~~
Many aspects of nature are cyclical- the seasons, the expansion of
species, day and night and others. One of the most universal cyclical
phenomena
is the spectrum of electromagnetic radiation which involves frequencies from
several hundred cycles per second ( naval sub radio ) to the most active
sub-atomic particles. Light is a high frequency electromagnetic radiation, as
is infrared (heat ). X-ray, and even the mass of the atomic proton.
Zero cps electricity is the familiar DC which is produced by chemical
reactions between dissimilar metals when subject to ionization. Flashlight
cells are typical- zinc and carbon being the two metals and an acid being the
medium. The output, if charted or graphed is a straight line at a constant
height ( battery voltage ) above or below the zero line. DC is always polar,
requiring care in hook up to avoid equipment and battery problems. DC may also
be generated from AC by special diode circuits such as the little black box
used to charge your radio equipment from AC.
60 cps electricity is the stuff that comes out of the AC jacks ( wall
sockets ) around your house. In a cycle, which takes 1/60 of a second, the
voltage starts at zero- rises to a max plus- returns to zero- declines below
zero to a max negative and then returns to zero. If graphed is the sine
wave of
mathematics. Little bleeps of power are delivered to your TV, first a positive
bleep and then a negative bleep- all within 1/60 second. Since power is
voltage
times current ( P=EI ) or P=IRxI and IxI is positive even when I is negative,
AC produces positive continuous power. Most AC is produced by rotating
machines
or vibrating electronic systems or electromechanical systems.
The relationship between frequency (f) and wave length (mu) is f x
mu = C, where C is a constant. Frequency is the number of cps of the AC,
mu is
the distance, at the speed of light, the wave will travel in one cycle and C
is the speed of light (300,000,000 meters per second). So, the wave length
mu =
300,000,000 mps/f in cps. We are dealing only in meters and seconds so the
wave
length will be in meters. As an example we can calculate the wave length of a
50.0 megacycle radio signal: mu = 300 mega-meters per second/50 megecycles per
second = 6 meters. The wave length of the higher and more energetic
frequencies may be only a few billionths of a meter; visible light wave
lengths
are much longer than x-ray wave lenghts and a great deal shorter than the
50 mc
- 6 meter wave length, yet each and all are electromagnetic radiations.
When the xmtr is on, the radiated frequency is impressed on the bottom
end of the antenna. Instantly an electrostatic impulse travels to the top of
the antenna (1/4 wavelength), and is then reflected back to the base of the
antenna. At the same time a magnetic impulse starts at the base, but is
delayed
and arrives 1/4 wave later at the top of the antenna. Thus on the antenna
exists (at the xmtr freq) an electrostatic and a magnetic impulse. The two
impulses, although the same frequency, are out of phase with each other;
exactly what is required to produce an electromagnetic radiation. This
radiation leaves the antenna at the speed of light and can travel many
thousands of miles.
The antenna on your transmitter is a 1/4 wave antenna and for 50 mc
radiation is 6 meters divided by 4 or 3/2 of a meter long; for 72 mc is
slightly shorter. These antennas are part of the tuned circuit in the
output of
the transmitter and should not be trimmed or detuned- pull out your antenna
for
any flight. The antenna on the receiver is also part of a tuned circuit, so do
not fold, bend, cut , staple or mutilate.
~~Basic Electricity, Part 06~~
This paper will be the last of the basic electricity series. The
series
was meant to casually give you a fast look at electricity. If you are
interested in pursuing the subject try library books on basic DC and basic AC
electricity. Some of the books may present both DC and AC in the same book.
Also review basic math, which pops up throughout the study of electricity. I
will be glad to discuss with you any uncertain areas which may bother you.
Kit building of electronic devices is a good way to get sucked into
enjoying electrical activity and will expose you to all of the standards and
conventions ( resistor and capacitor value color coding, reading drawings, how
to solder, what various parts look like, etc. ); those things which can
best be
learned only by doing.
I will admit that I lack a working knowledge of the solid state
technology ( transistors ) and the digital design technology ( cpu chips,
logic
chips and counters ), but had enough background to know when and how to
hire a
good man to do that work. My basic education was in the good old days of the
electron tubes which was a good exposure to the ideas and schemes which are
now accomplished by using solid state instead of tubes. Modulation is
modulation either by tubes or solid state. I am glad to have had the dirty old
mean engineer exposure to grid leak.
There is a great deal of satisfaction and fun in electricity at either
the hobby or professional level. Try it out.
~~ BE SAFE~~
~~~ Stuart ~~~
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