ELEN 236
Series and Parallel Circuits
www.okanagan.bc.ca/electronics
Series Circuits and Kirchoff’s Voltage Law
Reference
 All About Circuits->DC->Chapter 5 and Chapter 6
Questions:
 CurrentVoltageResistance: Qs: 70 – 110 (70-85, 86-99, 100-110)
Series Circuit Definition

Circuits (or portion of a circuit) where components are connected back to
back
o Share one point

Question to get you to start identifying distinguishing characteristics of
“series” circuits

In a series circuit, the voltage supplied by the source(s) is all used up by the
load(s) (Voltage gains = Voltage drops)
In a series circuit, the current is equal through all of the components
In a series circuit, the individual resistances add up to the total resistance
In a series circuit, the power individual power dissipations equal the total
power supplied



1
ELEN236. Series and Parallel Circuits
 e.g.: Build a circuit using the PHeT CCK.
How Would I prove each of the above points?
o measure current at all points. Should all be the same
o measure voltage across each component. Should sum to zero
o Calculate powers for each component. Should sum to zero
o Calculate total resistance. Calculate total current. Calculate current
for each individual component.

1)
2)
3)
Another way to state each of the above rules:
Sum of Vrises = Sum of Vdrops
Itotal = I1 = I2 = I3 …
Rtotal = R1 + R2 + R3 …


These statements are true no matter what is in the circuit.
e.g.:

Compare the direction of current through all components in this circuit with
the polarities of their respective voltage drops.

What do you notice about the relationship between current direction and
voltage polarity for the battery, versus for all the resistors?

How does this relate to the identification of these components as either
sources or loads?
2
ELEN236. Series and Parallel Circuits

Calculate Voltage Across each of the resistors in this circuit (Magnitude and
polarity). Also show the direction of current:
o Calculate power generated by source
o Calculate power dissipated by each component
Steps:
o
o
o
o
o
o
Find Total R of circuit
Calculate direction and magnitude of current (I = V/RT)
Calculate polarity and each VR (VR = I*R)
Calculate power delivered by source (Vsrc*I)
Calculate power dissipated by each component (VR*I)
Vsrc*I should equal sum of individual VR*I
Example
14 V
780 Ω
R1
R3
3.3 kΩ
R2
1.5 kΩ
R1
R2
R3
780 Ω
1.5 kΩ
3.3 kΩ
Total
V
I
R
P
(01957)
3
ELEN236. Series and Parallel Circuits
R1
V 1.957
I 2.509mA
R 780Ω
P 4.910mW
R2
3.763V
2.509mA
1.5kΩ
9.442mW
R3
8.280V
2.509mA
3.3kΩ
20.77mW
Total
14V
2.509mA
5.58kΩ
35.13mW


What are some ways that you could check your work?
Without performing any mathematical calculations, determine the effects on
all the component voltage drops and currents if resistor R1 were to fail open.

Without performing any mathematical calculations, determine the effects on
all the component voltage drops and currents if resistor R1 were to fail
shorted.
Example showing the effect of changing resistance in a series circuit:
SW1


SW2
SW3
(00295)
What will happen in this circuit as the switches are sequentially closed
starting with #1 and working to #3?
Describe how the successive closures will affect
o Total Circuit Resistance “seen” by the battery
o Total amount of current drawn from the battery
o The current through each resistor
o The voltage drop across each resistor
Example: Designing a series circuit using LED.
 LED description: rugged, efficient sources of light
 Not resistive when turned on the drop a (nearly) constant voltage
 Naïve LED circuit:


What can be put in to the circuit to limit the current.
o A resistor
A typical LED current is 20mA. Design LED circuit to give you 20mA
through LED which has a forward voltage drop of 2Volts.
4
ELEN236. Series and Parallel Circuits
Kirchoff’s Voltage Law

The concept that around any electrical loop the sum of the voltage rises
equals the sum of the voltage drops is formalized in Kirchoff’s Voltage Law:

Another way to put this is that if you start at one point on the circuit and go
around the circuit, everytime you go up in voltage, add the voltage, and
everytime you go down in voltage you subtract it.
o When you return back to where you started, your total should be at
zero
o Analogous to going for a hike in the mountains and returning to the
place you started.
 During your hike, you will sometimes be climbing upwards,
sometimes be climbing downwards, and sometimes walking
on the flat. When you return to the start your net elevation
gain is 0.
o It is basically a conservation of energy equation. It takes energy to
boost the voltage and things that dissipate energy drop voltage.
Single Loop Examples:
Determine the voltage polarity and magnitude of each component in these loops
and show that the sum of the voltages in the loop is equal to zero.
5
ELEN236. Series and Parallel Circuits
Two Loop Introduction
In this case, relative to the source, R2 is in parallel to R3 and R4. We will look at
how to solve for the voltages in this type of circuit soon (after we look at parallel
circuits).
Voltage Dividers
One of the reasons for having a resistor that was mentioned in the section on
resistors is to “split a voltage into proportions”. In other words, if you have a
voltage from a source, you may want to obtain some fraction of this voltage for a
particular purpose (e.g. a Voltage Reference).
Another example is in a sensor system as shown here:
o this example is a light sensor system.
o In this system, if the light level falls below a certain reference an LED is
turned on
o The circuit looks like this:
6
ELEN236. Series and Parallel Circuits
o LDR: Light dependent resistor. The resistance of an LDR varies depending
on how much light falls on it. More light means lower resistance
o Comparator: an electronic device that outputs a high voltage if the ‘+’ input
is at a higher voltage than the ‘-‘ input. Other wise it outputs a low voltage.
In this case assume “high voltage” means 5 volts and low voltage means 0
volts.
o In this circuit are two examples of series circuits where resistors are used to
provide proportion of the total (source) voltage to some other part of the
overall circuit.
o In this case the two Voltage Divider circuits are
o The circuit R1 and the LDR
 in this case the Voltage division is variable because the
resistance of the LDR is variable
o R2 and R3
 in this case the Voltage Division is fixed since R2 and R3 are
fixed
o Whenever a voltage source is applied across a number of resistors in
series, we know that the sum of the voltage drops will be equal to the
voltage source
o If R2 is 2 kΩ and R3 is 1 kΩ. Calculate the voltage that will be applied to
the ‘-‘ terminal of the comparator
Method 1
Method 2
7
ELEN236. Series and Parallel Circuits
o If the light falling on the LDR gave it a resistance of 11kΩ and R1 is 10kΩ.
Would the LED be on or off? (Remember if the voltage to the ‘+’ terminal is
higher than the voltage to the ‘-‘ terminal then the comparator output would
be 5 volts)
Voltage Divider circuits (or “voltage dividers”) can consist of more than one
resistor:
8
ELEN236. Series and Parallel Circuits
A Potentiometer Voltage Divider
Referring back to the light sensor circuit, how could you use a potentiometer to
make the reference voltage (trigger voltage) that turns the LED on variable?
Some More Example Problems
9
ELEN236. Series and Parallel Circuits
10
ELEN236. Series and Parallel Circuits
Parallel Circuits and Kirchoff’s Current Law (KCL)
Reference
 All About Circuits->DC->Chapter 5 and Chapter 6
Questions:
 CurrentVoltageResistance: Qs: 111 – 146 (11-122, 123-132, 133-146)
Parallel Circuit Definition

Circuits (or portion of a circuit) where components share two points-

Question to get you to start identifying distinguishing characteristics of
“parallel” circuits
A
B
C
D
F
E
11
ELEN236. Series and Parallel Circuits
The main things to keep in mind related to parallel circuits
 1) In a parallel circuit, the voltage drop across each of the parallel paths is
equal
 2) The amount of current flowing in to a node is equal to the amount of
current flowing out of the node
o A node is simply a junction in a circuit where two or more paths
connect
o e.g

3) In a parallel circuit, the inverse of the total resistance across the
connecting nodes in the circuit is equal to the sum of the inverses of the
resistances of each of the individual paths
 e.g.: Build a circuit using the PHeT CCK.
How Would I prove each of the above points?
o measure voltage across each component. Should all be the same
o measure current in out of each node and current in to each node.
Currents in should be equal to currents out
o Calculate powers for each component. Should sum to zero
(assuming sources are positive and loads are negative)
o Calculate total resistance. Calculate total current. Calculate current
for each individual component.
Proof for point 3 above:
12
ELEN236. Series and Parallel Circuits
Some Examples:
Qualitatively compare the currents through and voltages across each of these
lamps:
6 volt
bulb
6 volt
bulb
6 volt
bulb
+
6 volt
battery
_________________________________
According to Ohm’s Law, how much current goes through each of the resistors in
this circuit:
Trace the path of current in the circuit.
13
ELEN236. Series and Parallel Circuits
_________________________________
Calculate the total amount of current supplied by the voltage source:
Then calculate the total resistance that the voltage source must “see” in order to
create that much current.
Explain why the total resistance is less than either of the individual resistances.
_________________________________
In this circuit, calculate the current through each resistor. Then use P=VI to
calculate the power dissipated by each resistor and the power “generated” by the
voltage source.
_________________________________
Do the same thing for this circuit:
14
ELEN236. Series and Parallel Circuits
Note that the lowest valued resistor dissipates more power. This may seem
paradoxical, but the lower the value of the resistor, the larger the load that it will
place on the source. Another way to look at this is that a heavy load draws more
current, since for the same voltage source, a lower resistance will draw more
current, a lower resistance represents a heavier load.
_________________________________
What will happen to the brightness of the bulb when the switch is closed:
_________________________________
Calculate the total resistance between A and B:
_________________________________
Without doing any calculations, which would have more effect on RAB, adding a
fourth parallel resistor with R=1Ω or R=1MI Ω ?
_________________________________
Suppose you needed to create a resistance of precisely 197Ω for a precision
measurement device, but all you had were a 1000 Ω resistor and a rheostat
15
ELEN236. Series and Parallel Circuits
(variable resistor) with a resistance range of 200-300 Ω. How would you create
your precise resistance?
_________________________________
What is wrong with the measurements in this circuit?
+
4A A
+
3A A
-
+
5A A
-
_________________________________
Kirchoff’s Current Law
Pretty much already covered:
 CurrentIntoTheNode   CurrentsOutOfTheNode
Another way to look at KCL: “What goes in must come out!”
16
ELEN236. Series and Parallel Circuits
Series and Parallel Circuits
o Generally a circuit is not going to be only a series circuit or only a parallel
circuit. It will usually be a combination of some parts of the circuit in series
and some part of the circuit in parallel.
o to analyze such circuits, just keep all of the rules about circuits in mind:
1)
2)
3)
4)
Elements in series will have the same current going through them
Elements in parallel will have the same voltage drop across them.
In a circuit loop, the voltage rises will equal the voltage drops (KVL)
At a node, the currents in will equal the currents out (KCL)
Identify which of these components are connected directly in series with each other
and which are connected directly in parallel with each other:
Figure 1
Figure 3
Figure 2
R1
R1
R2
R1
R3
R2
R2
R3
R3
Figure 4
Figure 5
Figure 6
R1
R1
R3
R1
R3
R2
R2
R4
R2
R4
R3
17
ELEN236. Series and Parallel Circuits
Figure 1
Figure 2
SW1
R2
C1
R1
R4
Figure 3
C1
R3
L1
R2
R1
R1
Figure 4
Figure 5
C1
X1
L1
R2
L2
L1
C1
Figure 6
R2
R1
R4
R3
R1
Some equivalent resistance questions:
For these questions, just go through and combine series R’s into one equivalent R
and parallel R’s in to one equivalent R. Continue doing this until you have one
equivalent R left.
____________________________________________
18
ELEN236. Series and Parallel Circuits
____________________________________________
_____________________________________
19
ELEN236. Series and Parallel Circuits
___________________________________________
Rank these 5 light bulb circuits in order from least resistance to greatest
resistance:
A
D
B
E
C
(00039)
Calculate the resistance between points A and B (RAB) for each of the following
resistor networks:
Class does these ones:
20
ELEN236. Series and Parallel Circuits
Figure 1
All resistors 500 Ω
Figure 2
Figure 3
All resistors 1 kΩ
A
B
A
2 kΩ
5 kΩ
B
100 Ω
470 Ω
B
A
Figure 4
Figure 5
250 Ω
All resistors 2.2 kΩ
A
B
Figure 6
A
220 Ω
470 Ω
470 Ω
100 Ω
330 Ω
A
940 Ω
1: 500 Ω
B
B
(01757)
2: 750 Ω
3: 1.511k Ω 4: 940 Ω
5: 880 Ω
6: 80.54Ω
Think about how you approached each of these problems, and let the entire class
participate in the reasoning process. The point of this question, like most of the
questions in the Socratic Electronics, is not merely to obtain the correct answers,
but to stimulate understanding of how to solve problems such as these.
Complete the table of values for this circuit:
2.2 kΩ
6.8 kΩ
R2
1 kΩ
R1
R4
R3
470 Ω
6 volts
R1
R2
R3
R4
Total
V
I
R
P
1 kΩ
2.2 kΩ
470 Ω
6.8 kΩ
(01756)
21
ELEN236. Series and Parallel Circuits
R1
R2
R3
R4
Total
V
1.649 V
3.627 V
725 mV
725 mV
6V
I
1.649 mA
1.649 mA
1.542 mA
107 μA
1.649 mA
R
1 kΩ
2.2 kΩ
470 Ω
6.8 kΩ
3.64 kΩ
P
2.718 mW 5.979 mW 1.117 mW 77.24 μW
9.891 mW
Think about and outline your problem-solving strategies for this kind of problem. I
may give you an opportunity to explain your methods and to see other methods of
solution. An especially good point to think about how would you go about
checking your work to see if any mistakes were made.
Practice Problems: 149, 151, 152, 154, 156, 158, 159, 163, 165
22