Here is the "Electricity  Basic Navy Training Courses"
(NAVPERS 10622)
in its entirety. It should provide one of the Internet's best resources for people seeking
a basic electricity course  complete with examples worked out. See
copyright. See
Table of Contents. • U.S. Government Printing Office; 1945  618779
Chapter 8 of the U.S. Navy's basic electronics course
of study, titled "The Series Circuit: Why Know Circuits?" introduces the concept of series
electrical circuit analysis. After discussing basic characteristics and applications
of resistors, capacitors, inductors, conductors, and insulators, analyzing series circuits
are traditionally the beginning point for fledgling technicians, scientists, hobbyists,
and engineers. Purely resistive series circuits have just one current path with the same
value through every component, making calculations extremely simple. Things start getting
a bit tougher when reactive components are introduced, but simple trigonometry takes
care of that. The move into parallel circuits is typically the first barrier that washes
out students least likely to succeed. A few guys in my USAF tech school had to change
career fields after about the third weeks of Basic Electronics because they could not
grasp parallel circuit analysis. One switched to being a Pavement Maintenance Specialist
and got assigned to Minot AFB in North Dakota patching holes in the runway from B52
wheels.
Chapter 8: The Series Circuit  Why Know Circuits?
You have a good chance to outrank the bull in
the China shop  just try fooling around with circuits before you know what you're doing!
After burning up a few instruments at one hundred dollars per copy, you'll probably wind
up electrocuting yourself or your shipmates!
Electrical circuits are the power carriers of the electrical system. When they are
connected properly, they are efficient and trouble free. BUT, foul them up by improper
connections and they'll put your whole system out of commission.
The few circuits you have been made acquainted with are SIMPLE circuits  only a source,
its load, and the connecting wires. Few practical circuits can be so simple. For example,
it would be a terrific waste if EVERY electrical load had its OWN generator and its OWN
feeders. Imagine the confusion of cables, lines, and wires if every light, every motor,
every telephone, every heater, had its own separate feeder lines directly from the dynamo
room. For reasons of ECONOMY and EFFICIENCY, therefore, most circuits are, actually VERY
COMPLEX. They are designed so that ONE generator can feed MANY electrical loads. But
no matter how complex any particular circuit becomes, it is one of three general types
 the SERIES, the PARALLEL, or the SERIESPARALLEL.
Every electrical load is designed to contain a specific resistance and operate at
a certain rated voltage. The resistance of the road controls the amount of current at
the rated voltage. The proper type of circuit connection insures the load of its rated
voltage and current. Imagine the fireworks if a searchlight got 200 volts instead of
95 volts. Or  you'd wait a long time for chow from a 220 volt galley stove connected
on a 110 volt line. Both these things could happen by using incorrect connections.
VOLTAGE IN SERIES CIRCUITS
The first typethe series circuit is a ONEPATH circuit. You can always recognize
a series connection by two factsit will NEVER HAVE MORE THAN ONE CONDUCTOR CONNECTED
TO ANY TERMINAL, and you will find only ONE PATH from source to load (or loads) and back
to source.
Figure 37 shows a simple series circuit. In A, a voltmeter is connected across the
total resistance. It reads the TOTAL voltage drop of the TOTAL resistance  in this case,
6 volts. NOTICE that the voltage drop which occurs in the wires is ignored. This is standard
practice for short wires because the resistance is very small. But for longer wires,
connecting load and source, the resistance is large and the voltage drop is appreciable.
It must be considered in the circuit. In B, the voltmeter is connected across only HALF
the resistance. In this case, the voltmeter reads onehalf of 6 volts or 3 volts, indicating
that HALF voltage is used for HALF the resistance. Now connect two voltmeterseach one
across half the resistance  as in C. Each voltmeter reads 3 volts. This gives you the
law for voltage drops in a series circuit. THE TOTAL VOLTAGE IN ANY SERIES CIRCUIT IS
THE SUM OF ALL THE VOLTAGE DROPS. Mathematically the law says 
Figure 37.  Voltage in a series circuit.
Figure 38.  Voltages across separate loads.
E_{t }= E_{1 }+ E_{2
}+ E_{3}, etc.
when 
E_{t }= the total voltage;
E_{1} = the voltage drop of the first load;
E_{2 }= the voltage drop of the second load;
E_{3} =the voltage drop of the third load.
In figure 37, E_{3} is 0; hence,
E_{t }= E_{1 }+ E_{2} + E_{3},
etc.
6 v. = 3 v. + 3 v. + 0
Two more examples of series circuits are shown in figure 38. In A, three equal resistors,
of 4 ohms each, are connected in series. The voltmeters indicate that it requires 2 volts
to force the current through each resistor. Notice that the total voltage is equal to
the sum of all the voltage drops 
E_{t }= E_{1} + E_{2} + E_{3}, etc.
E_{t} = 2 + 2 + 2 = 6 v.
In B of figure 38, two UNEQUAL resistances are connected in series. In this case,
the voltage drops are not equal  THEY ARE PROPORTIONAL TO THE RESISTANCE. Again 
E_{t }= E_{1} + E_{2} + E_{3}, etc.
12 v.= 3 v. + 9v.
The searchlight circuit is a good example of this principle of a series circuit. The
ship's voltage is usually around 120 volts. But the standard voltage for the Navy's largest
searchlight is only 80 volts. In order to reduce the 120 volts to the operating standard
of 80 volts, a resistor is placed in series with the light. This resistor uses up about
40 volts, leaving a drop of 80 volts for the light. (120 v. = 40 v. + 80 v.).
Current in Series Circuits
Figure 39.  Control in a series circuit.
There is only one path for current in a series circuit. And the amount of current
passing any point in the circuit is the same as the amount of current passing any other
point in the circuit. This gives you the law for current in a series circuit. THE CURRENT
IN A SERIES CIRCUIT IS THE SAME IN ALL PARTS. Or mathematically 
I_{t }= I_{1} = I_{2}= I_{3},
etc.
when 
I_{t} = total current;
I_{1} = current through the first load;
I_{2} = current through the second load;
I_{3} = current through the third load.
Suppose you connect a lamp, a switch, and a motor in series as in figure 39. The current
through each part of the circuit is the same.
If the switch is opened the current through the switch becomes zero  open circuit.
Likewise, the current through both the motor and the lamp be come zero. The opened switch
"shutoff" the loads. Switches CONTROLLING electrical loads are ALWAYS in series with
the loads. In the same circuit, imagine that the lamp is broken. A broken lamp is also
an open circuit and would stop the current through the motor and the switch. For this
reason, two loads which are intended to be INDEPENDENT of each other, are NEVER connected
in series.
Resistance in Series Circuits
Figure 40.  Resistance in series.
Two resistances are connected in series in figure 40. Tracing the circuit, note that
the current passes first through one resistor 'and then through the other. This means
that the current is opposed by the force of both resistances. In figure 40, each load
has a resistance of 10 ohms, but since the current passes through BOTH loads, the total
opposition to current is 20 ohms. This gives you the law for resistances connected in
series  THE TOTAL RESISTANCE IN ANY SERIES CIRCUIT IS EQUAL TO THE SUM OF ALL THE INDIVIDUAL
RESISTANCES. Mathematically this says 
R_{t }= R_{1} + R_{2} + R_{3},
etc.
when 
R_{t} = total resistance,
R_{1} = resistance of the first load;
R_{2} = resistance of the second load;
R_{3} = resistance of the third load.
In the problem of figure 40 
R_{t}=R_{1}+R_{2}
20 Ω=10 Ω+10 Ω
This principle is employed in limiting the amount of current through a load by inserting
resistors in series with the load. For example, the rated amperage through the lamp in
figure 41 is 2 amperes. The lamp itself has 40 ohms resistance; but on a 120 volt line,
40 ohms will permit 3 amperes to pass 
Figure 41.  Controlling current by series resistance.
I = E/R = 120/40 = 3 amps.
This means that, as long as the lamp is operated on 120 volts, it will pass 3 amperes.
And 3 amperes in a 2 ampere lamp will melt the filament (burn it out) . You can see that
more. than the lamp's 40 ohms of resistance is required to reduce the current to its
safe value of 2 amperes. Using Ohm's law to calculate the total resistance required to
limit the current to 2 amperes 
R = E/I = 120/2 = 60 Ω
This means that a 20 ohm resistor would have to be added in series to the 40 ohms
of the lamp. Then the total resistance is 60 ohms 
R_{t }= R_{1} + R_{2}
60 Ω = 40 Ω + 20 Ω
Now the current is limited to 2 amperes.
Keep off the Rocks
Here are a few simple rules that will help keep you off the rocks 
1. Draw a schematic of your problem.
2. Label each value on the schematic that is known.
3. Determine WHAT it is that you want to know. Is it the CURRENT, VOLTAGE, RESISTANCE,
POWER, EFFICIENCY, INPUT OR OUTPUT?
4. Select the equation for your solution and use the EASIEST form of the equation.
If you are looking for CURRENT, use I = E/R. If you are looking for VOLTAGE, use E =
IR. If you are looking for RESISTANCE, use R = E/I.
5. (IMPORTANT) Apply the law to either a PART or the WHOLE circuit. DON'T MIX UP YOUR
VALUES. If you are looking for the resistance of a PART of a circuit, use the values
or current and voltage for that PART. If you are looking for the TOTAL resistance, use
the values of current and voltage for the TOTAL circuit.
6. Substitute the numerical values in your equation and solve.
Figure 42.  Ohm's law. Figure 43.  Power equation.
You've been given a pretty big dose of formulas and equations all at once. They're
hard to take  so, here's a "crutch" to help you over the rough spots. When you have
a problem in current, voltage, or resistance sketch a "pie" and divide it into three
pieces. Label each piece as in figure 42. Now, using your finger, cover up the quantity
you want to know. What's left is the formula for solving for that quantity.
For example, if you want to know current, cover I; E/R remains, and I = E/R. If you
want to know the voltage, cover E; IR remains, and E = IR. Likewise, if you want to know
resistance, cover R; E/I remains, and R = E/I. You can make the same kind of "pie" for
the power equation. It's shown in figure 43.
Simple, isn't it? Let's try it on a few problems.
Problems in Series Circuits
The BEST (not always the easiest) way to get a clear understanding of circuits is
to work circuit problems. You will learn a lot by going through each of the examples
which follow. Each example has been selected to illustrate a practical circuit problem.
EXAMPLE 1 
Figure 44.  Example 1.
Figure 45.  Example 2.
Three lamps are connected in series. Each has a resistance of 60 ohms. A generator
producing 120 v. of emf powers the circuit. What is the total current in the circuit,
and what is the current through each lamp?
Rule 1. Sketch the circuit  figure 44.
Rule 2. Label values.
Rule 3. What is wanted? I_{t}, I_{1}, I_{2} and I_{3}.
Rule 4. Use I = E/R
Rule 5. Use I = E/R first, for the TOTAL current, and then, for the current of EACH
LAMP.
Rule 6. Use I_{t} = E_{t}/R_{t} = 120/180 = 2/3 amp.
(for I_{t}) (R_{t}
= R_{1} + R_{2} + R_{3})
(for I_{1}, I_{2} and I_{3}) E_{1}/R_{1} =
40/60 = 2/3 amp. (Voltage divides in a series circuit)
Is it strange that the answers are the same? No  I_{t} = I_{1} =
I_{2} = I_{3} in a series circuit. Therefore, the total current is equal
to the part currents. You will learn to make use of short cuts like this. But until you
are sure of what you're doing, it's. best to be complete AND CORRECT. Suppose you had
slipped up on Rule 5 (using a combination of a PART and the WHOLE). Say you had used
the TOTAL voltage and the resistance of a PART. See what happens 
I = E/R = 120/40 = 3 amps. ABSOLUTELY WRONG.
EXAMPLE 2 
Two lamps are connected in series on a 240v. line. One lamp has 40 ohms resistance,
the other has 80 ohms resistance (see figure 45). What is the total current and power?
What is the current and power of each lamp?
I_{t} = E_{t}/R_{t} = 240/120 = 2 amps.
I_{t} = I_{1} = I_{2} therefore I_{1} = I_{2}
= 2 amps.
P_{t} = E_{t}I_{t} = 240 x 2 = 480 w.
The power of each of the two lamps can be found in two ways.
(1) Find the voltage drop across each lamp 
(RF Cafe note: original had E_{1} and E_{2}
reversed)
E_{1} = I_{1} x R_{1} = 2 x 40 = 80 v.
E_{2} = I_{2} x R_{2} = 2 x 80 = 160 v.
Then  (RF Cafe note: original
had P_{1} and P_{2} reversed  thanks to Lou N.)
P_{1} = E_{1} x I_{1} = 80 x 2 = 160 w. (RF Cafe note: original had
E_{2} x I_{2)}
P_{2} = E_{2} x I_{2} = 160 x 2 = 320 w.
OR 
(2) In the equation P = EI, substitute for E the value of IR.
Figure 46.  Example 3.
Then (RF Cafe note: original
had P_{1} and P_{2} reversed  thanks to Lou N.)
P = I x IR, or P = I^{2}R
P_{1} = I_{1}^{2}R_{1} = 4 x 40 = 160 w.
P_{2} = I_{2}^{2}R_{2} = 4 x 80 = 320 w.
Example 3 
Figure 46 shows three 1,000 watt heaters connected in series to a 240volt battery.
Each heater has a current of 12.5 amperes. (1) What is the total resistance? (2) Resistance
of each heater? (3) Total current? (4) Total power?
(1) R_{t} = E_{t}/I_{t} = 240/12.5 = 19.2 Ω
(2) R_{1} = P_{1}/I_{1}^{2} = 1,000/(12.5 x
12.5) = 1,000/156.25 = 6.4 Ω
R_{1} = R_{2} = R_{3} (equal power  all are
1,000 w.)
R_{1} = R_{2} = R_{3} = 6.4 Ω
(3) I_{t} = I_{1} = I_{2} = I_{3} = 12.5 amps.
(4) P_{1} = E_{1}I_{1} = 240 x 12.5 = 3,000 w.
or P_{t} = P_{1 }+ P_{2} + P_{3} = 1,000
+ 1,000 + 1,000 = 3,000 w.
Chapter 8 Quiz
(click here)
