Series Circuits
Lecture Study Material
Resistors in Identifying component interaction in a circuit is an important aspect of being a technician or
engineer. To have components in series, the same current must flow through each of the
Series
components. Stated differently, series circuit current has only one path to flow from the sources
negative terminal through the circuit components to the positive terminal of the power source (the
current is the same everywhere in a series circuit). An easy way to evaluate the circuit is to use your
finger to trace current flow. Start at the negative terminal of the power source and move your finger
along the path of current flow towards the positive terminal of the power source. As your finger
moves from one component through another following the current flow means that these
components are in series.
1kohm
Es
5.6kohm
2.2kohm
In the above circuit, place your finger on the negative terminal of the power source. Move it
following the connection wire to the left-side of the 2.2k ohm resistor, through it and through the
5.6k ohm and the 1k ohm resistors back to the power source's positive terminal. Because the same
current flows through all three resistors they are in series. Do the same thing to the following circuit.
Notice that the same current does not flow through R1 and R2 (there are two paths of current flow
from the negative to positive terminals of the power source), therefore they are not in series.
R1
680ohm
R2
Current in a "The current is the same though all points in a series circuit". The current flowing through one
Series Circuit component will be the same that flows through all other components in the series circuit. This is a
very important concept. The current will always be the same if components are in series. We will use
this to help solve circuit problems. If R1 in the following circuit has a current value of 7.58mA flowing
through it then R2, R3, and R4 also has a current flow value of 7.58mA.
Conservation
of Energy
or
Kirchhoff's
Voltage Law
Energy cannot be created nor destroyed - energy can only be converted from one of its forms into
another form. In electronics we use Kirchhoff's laws to represent this fact in circuits. Kirchhoff's
voltage law states: "The algebraic sum of the voltages in any closed loop must equal zero". Whatever
voltage supplied by a source in a circuit must be used by the loads in that circuit. Using the
convention of going from a positive (+) to a negative (-) potential assign a plus (+) sign to that
components voltage value. Likewise, if going from a - to a + potential assign a negative (-) sign to that
components voltage value. Current will flow from the negative terminal towards the positive
terminal producing the potentials shown in the diagram below. Start Kirchhoff's voltage law
equation at point "A", the positive terminal of the power source, writing the voltage values with its
sign using the convention previously stated; the voltage law equation for this circuit will be:
A
+
R1
-
5.6kOhm
+
Es
100 V
+
-
-
+
-
R4
1kOhm
+
R2
5.6kOhm
R3
1kOhm
Rearrange the equation:
The voltage drops of R1, R2, R3, and R4 (identified as VR1, VR2, VR3, and VR4) must equal the source
voltage (Es) of 100V.
Ohm's law states that voltage is equal to current times resistance (V=IR). Using Ohm's law to modify
the circuit equation developed above will yield the following equivalent equation:
The current is the same everywhere; therefore the I on the
right-side of the equation is the same as on the left-side so
they cancel. We now have the basic equation for resistors in
series. This equation simple states that the resistance of any
number of resistors in series can be combined by simple
addition to form one equivalent resistive component. This type
of simplification is the key (secret) to solving complex circuit
problems. Instead of having four loads, the equivalent circuit
now has only one and all the source voltage has to be used by
RT. Knowing the voltage the load must use allow us to use
Ohm's law to determine the circuits current as you will see
later in this unit.
Es
100 V
Finding
Circuit
Values
RT
13.2kOhm
Knowing the currents magnitude in a series circuit is very important, because of the current being
the same everywhere. That means if we know the current value for one component we know the
value for all components, which will allow us to determine other circuit parameters. In the example
circuit used to determine RT, Es = 100V and RT = 13.2k ohms; using Ohm's law the current can now
be determined.
RT
13.2kOhm
Es
100 V
ES
100V
I= ⇒
7.58 ×10−3 A ⇒ 7.58mA
=
RT
13.2 K Ω
Now knowing the current in this circuit is 7.58mA will allow us to determine the voltage drops in the
original circuit for R1, R2, R3, and R4.
A
+
R1
-
5.6kOhm
+
Es
100 V
+
-
-
+
R2
5.6kOhm
R3
1kOhm
-
R4
+
1kOhm
Using Ohm's law:
You will usually see small differences because of rounding that is done in each of the calculations;
the more calculations done in a problem usually will mean larger differences. For this problem six
one-hundreds of a volt compared to 100V is a pretty small difference.
Voltage
Dividers
A rose by any other name is still a rose! A series circuit can be called a voltage divider, but it still is a
series circuit. It depends on what the circuit is designed to perform. Many times it is necessary to
step a power source down to a value that is required by some type of load. A radio requiring 9V to
operate cannot be powered by a 12V battery, but if we design a circuit so that the radio gets 9Vs and
a dropping resistor gets 3V - Kirchhoff's voltage law will still hold true and the voltage to the radio
will be what is required for it to operate. This type of circuit is referred to as a "voltage divider
circuit" instead of a series circuit.
R1
A
B
5.6kohm
Es
100V
R2
5.6kohm
C
R3
1kohm
R4
D
1kohm
The circuit shown to the right is a voltage divider circuit - it is dividing the voltage supplied by the
power source into four separate voltage values. The secret in solving for the resistor voltage drops is
knowing that the current is the same everywhere in all series circuit.
and
Knowing the voltage value and resistance of one component, will allow you to determine another components
voltage drop. Hopefully you can see from the above equations that everything is proportional. Knowing that
the source voltage (Es) equals 100V and its associated resistance RT can easily be determined to be 13.2kΩ will
allow us to determine a voltage drop across another component. This process is no different that using Ohm's
law to find current and then to multiply the current by each resistance value to calculate the components
voltage drop. The problem here is that to do so will require the execution of two calculations and two roundoffs. The following process does the same thing, only that everything is embedded in one equation which will
only have one round-off - giving us a better approximation and requires less work. To remember the voltage
division rule use the following saying: to determine the voltage value of a component, divide its resistance
value by the resistance value of the component that has a known voltage drop value and then multiply by
that voltage value.
This example Es is known to be 100V and its associated
resistance is 13.2kΩ, use these values to determine the voltage
drop of R1 the 5.6kΩ resistor.
Determine the voltage value across R3. Check you
work using Kirchhoff's voltage law: 42.42V + 42.42V
+ 7.58V + 7.58V = 100V compared to the earlier
process which required more calculations whose
sum was 100.06V - this process gives us a little more
accuracy as well as saving us some steps.
Resistor
Power
Ratings
The resistors power rating is the maximum amount of power that that resistor can dissipate without
being damaged. The power rating of resistors is a component of their physical composition, size,
and shape. Usually the power rating of resistors is not printed or color-coded onto their bodies. One
must become familiar with their size and shape to make that determination. It is easy but will
require some experience evaluating resistors (see figure 4-5 of your textbook for resistor sizewattage comparisons). Most resistor used today will be made from metal film, these resistors will
not flame if they experience overheating (consuming more energy that they are designed to
consume).