Here are the key steps to solve series-parallel circuits: 1) Identify series and parallel sections 2) Use series/parallel rules within each section 3) Connect the sections using KVL and KCL Let me know if any part of the process is unclear! Solving complex circuits takes practice.

1. Physics 110
Fundamentals of
Electronics

2. Chapter 2
DC Networks

3. Review Topics
Scientific Notation
Units of Measure

4. What is Electricity?
From the Greek word “elektron”
that means “amber”
There are two types of electricity:
– Static Electricity - no motion of free charges
– Current Electricity - motion of free charges
» Direct Current (DC)
» Alternating Current (AC)

5. 2.2 Current
Current is the rate of flow of charge through
a conductor.
– Conductor
» materials with free electrons
» e.g. copper, aluminum, gold, most metals
– Insulator
» materials with no free electrons
» e.g. glass, plastics, ceramics, wood

6. 1

7. Equation for Current
I=Q/t
I = the current in Amperes (A)
Q = the amount of charge in Coulombs (C)
t = the time measured in seconds (s)
The charge of an electron is 1.6 x 10-19 C

8. Effect of Electric Currents on the Body
0.001 A can be felt
0.005 A is painful
0.010 A causes involuntary muscle contractions
0.015 A causes loss of muscle control
0.070 A can be fatal if the current last for more
than 1 second

9. Example Problem 2.0
How much charge will pass through a
conductor in 0.1 seconds if the current is
0.5 Amperes?
How many electrons are required for this
much charge?

10. Example Problem 2.1
Determine the current in amperes through a
wire if 18.726 x 1018 electrons pass through
the conductor in 0.02 minutes.
Example Problem 2.2
How long will it take 120 C of charge to
pass through a conductor if the current is
2 A?

11. Example Problem 2.3 and 2.4
Write the following in the most convenient
form using Table 2.1:
(a) 10,000 V
(b) 0.00001 A
(c) 0.004 seconds
(d) 630,000,000 Watts
(e) 0.00006 A

12. Wire Gauge?
AWG = American Wire Gauge
AWG numbers indicate the size of the
wire….but in reverse.
For example, No. 12 gauge wire has a
larger diameter than a No. 14 gauge wire.

13. 2.3 Voltage
Voltage is the measure of the potential to
move electrons.
Sources of Voltage
– Batteries (DC)
– Wall Outlets (AC)
The term ground refers to a zero voltage or
earth potential.

14. Digital Multimeters
Measurement Device Circuit Symbol
Voltage Voltmeter
Current Ammeter
Resistance Ohmeter

15. More on Batteries
Positive (+) and Negative (-) terminals
Batteries use a chemical reaction to create
voltage.
Construction: Two different metals and Acid
– e.g. Copper, Zinc, and Citrus Acid
– e.g. Lead, Lead Oxide, Sulfuric Acid
– e.g. Nickel, Cadmium, Acid Paste
Batteries “add” when you connect them in
series.
Circuit Symbol:

16. 1

17. Equation for Voltage
V=W/Q
V = the voltage in volts (V)
Q = the amount of charge in Coulombs (C)
W = the energy expended in Joules (J)

18. Example Problem 2.7
Determine the energy expended by a 12 V
battery in moving 20 x 1018 electrons
between its terminals.

19. Example Problem 2.8
(a) If 8 mJ of energy is expended moving
200 µC from one point in an electrical
circuit to another, what is the difference in
potential between the two points?
(b) How many electrons were involved in
the motion of charge in part (a)?

20. 2.4 Resistance and Ohm’s Law
Resistance it the measure of a material’s
ability to resist the flow of of electrons.
It is measure in Ohms (Ω).
Ohm’s Law:
V=IR
V or E = voltage
I = current
R = resistance

21. Example Problem 2.9
Determine the voltage drop across a 2.2 k Ω
resistor if the current is 8 mA.
Example Problem 2.10
Determine the current drawn by a toaster
having an internal resistance of 22 Ω if the
applied voltage is 120 V.

22. Example Problem 2.11
Determine the internal resistance of an
alarm clock that draws 20 mA at 120 V.

23. Equation for Resistance

R =ρ
A
ρ = resistivity of the material from tables
 = length of the material in feet (ft)
A = area in circular mils (CM)

24. Example Problem 2.12
Determine the resistance of 100 yards of
copper wire having and 1/8 inch diameters.

25. Concept Questions
How can you determine the current through
a resistor if you know the voltage across it?
How can you change the resistance of a
resistor?

26. Temperature dependence of Resistance
R 2 = R 1 [1 + α1 ( t 2 − t1 )]
R = resistances
t = temperatures
α = temperature coefficient from tables

27. Example Problem 2.15
The resistance of a copper conductor is
0.3 Ω at room temperature (20°C).
Determine the resistance of the conductor
at the boiling point of water (100°C).

28. 1

29. Resistor Color Codes
0 Black
1 Brown
2 Red Tolerance
3 Orange 5% Gold
4 Yellow 10% Silver
5 Green
6 Blue
7 Violet
8 Gray
Memorize this table.
9 White

30. Example Problem 2.17
Determine the manufacturer’s guaranteed
range of values for a carbon resistor with
color bands of Blue, Gray, Black and Gold.
Example Problem 2.18
Determine the color coding for a 100 k Ω
resistor with a 10% tolerance.

31. Total Resistance for Resistors in Series
R T = R1 + R 2
Total Resistance for Resistors in Parallel
1 1 1
= +
R T R1 R 2

32. Potentiometers
They are three terminal devices with a
knob.
The knob moves a slider which changes the
resistance between the terminals.
Circuit Symbols:

33. What is the difference between E and V?
E is the voltage supplied by a battery.
V is the voltage measured across a resistor.

34. 2.5 Power, Energy, Efficiency
Power is the measure of the rate of energy
conversion.
Resistors convert electrical energy into heat
energy.
Equation for Power:
P=IE Power Delivered by a Battery
P=IV Power Dissipated by a Resistor
What are some other ways that we can write
this equation?

35. Example Problem 2.19
Determine the current drawn by a 180 W
television set when connected to a 120 V
outlet.

36. Simple Circuit Problem
Using circuit symbols, draw a circuit for a
9V battery connected to a 10Ω resistor.
Draw and label the direction of
conventional current.
Now include a voltmeter in your sketch that
will measure the voltage drop across the
resistors. What will it read?
Include a ammeter that will measure the
current through the resistor. What will it
read?

37. Simple Circuit Problem
How much power does the battery deliver?
How much power does the resistor
dissipate?

38. 1

39. Note: Equations will be provided
on the chalk board during the
exam.
However, you must know what
each variable represents and
what units are used for each.

40. Example Problem 2.20
Determine the resistance of a 1200W
toaster that draws 10A.

41. Energy and power are related:
W=Pt
W = energy in Joules
P = power in Watts
t = time in seconds

42. Example Problem 2.21
Determine the cost of using the following
appliances for the time indicated if the
average cost is 9 cents/kWh.
– (a) 1200W iron for 2 hours
– (b) 160W color TV for 3 hours and 30 minutes
– (c) Six 60W bulbs for 7 hours.

43. Efficiency
Po
η = ×100%
Pi
Pi = Po + Pl
1hp = 746 W

44. Example Problem 2.22
Determine the efficiency of operation and
power lost in a 5hp DC motor that draws
18A as 230V.

45. 2.6 Series DC Networks
Two elements are in series if they have only
one terminal in common that is not connected
to a third current carrying component.
Total Resistance
R T = R 1 + R 2 + R 3 + ... + R N
Current through a Series
E
I=
RT

46. Consider Figure 2.29.
» E=24V, R1=2Ω, R2=4Ω, R3=6Ω
What is RT?
What is I?
What is V1, V2 and V3?
What is P1, P2, P3, and PE?

47. Kirchhoff’s Voltage Law
“The algebraic sum of the voltage rises and
drops around a closed path must be equal to
zero.”
∑ Vrises − ∑ Vdrops = 0

48. Voltage-divider rule
– “The voltage across any resistor in a series is some
fraction of the battery voltage.”
R xE
Vx =
RT

49. 1

50. Express these numbers with only
three significant figures and in the
most convenient form.
0.038457 C
0.0012878 A
12869.578 V
0.57382 W

51. 2.7 Parallel DC Networks
Two elements are in parallel if they have two
terminals in common.
Total Resistance
1 1 1 1 1
= + + + ... +
R T R1 R 2 R 3 RN
Source Current
E
I=
RT

52. Concept Test
For resistors in series, what is the same for
every resistor? R, V or I?
» Answer: I
For resistors in parallel, what is the same
for every resistor? R, V or I?
» Answer: V

53. Kirchhoff’s Current Law
“The sum of the current entering a junction
must equal to the current leaving.”
∑ I entering = ∑ I leaving

54. Example Problem 2.28
Using Kirchhoff’s current law, determine
the currents I3 and I6 for the system of
Figure 2.38

55. Consider Figure 2.32.
» E1=100V
» E2=50V
» E3=20V
» R1=10Ω
» R2=30Ω
» R3=40Ω
What is I?
What is V2?

56. Example Problem 2.25
Find V1 and V2 of Figure 2.33 using
Kirchhoff’s voltage law.

57. Voltage Sources in Series

58. Current-divider rule
– “The current through any resistor in parallel with
other resistors is some fraction of the source
current.”
IR T
Ix =
Rx

59. Example Problem 2.26
Determine the following for the parallel
network in Fig. 2.36.
– (a) RT
– (b) I
– (c) I2
– (d) P3

60. 2.8 Series-Parallel Networks
Example Problem 2.29
Determine the following for the network in
Fig. 2.41.
– (a) RT
– (b) I
– (c) I1 and I2
– (d) V1