Chapter 2
Series and Parallel Circuits – Part 1
PowerPoint® Slides
Edited by Dr Ng Jiunn Yea
(Jan 2023)
1
Outline of this Chapter

Ohm’s Law

Energy and Power

Series Circuits

Voltage Divider Rule

Kirchhoff’s Voltage Law

Other Notation

Application of Series Circuit
2
Ohm’s Law
3
Ohm’s law

Current through an ideal conductor is proportional to
the applied voltage:
𝑽 = 𝑰𝑹
Where 𝑉 is voltage in Volts
𝐼 is current in Amperes
𝑅 is resistance in Ohms
4
Ohm’s law (Example)

Calculate the voltage across a 120 Ω resistor if given current through
it is 0.25 𝐴.
Solution:
𝑉 = 𝐼𝑅 = 0.25 × 120
𝑉 = 30 𝑉

Calculate the current through the 2 𝑘 resistor if the voltage drop
across it is 16 𝑉.
Solution:
𝑉
16
=
𝑅 2000
𝐼 = 8 𝑚𝐴
𝐼=
5
Energy and Power
6
Energy
•
Energy, W, is the ability to do work and is measured in joules.
•
One joule is the work done when a force of one newton is
applied through a distance of one meter.
•
The symbol for energy, W, represents work, but should not be
confused with the unit for power, the watt, W.
▪
The kilowatt-hour (kWh) is a much larger unit of energy than
the joule.
▪
There are 3.6 x 106 J in a kWh.
Energy (Wh ) = power (W )  time(h)
power (W )  time(h)
Energy (kWh ) =
1000
7
Power

Power is an indication of how much work can be done in a specified
amount of time.
W
P=
t
OR
P = IV

Power is measured in watts (or kilowatts).

Two other equations for power in circuits that are collectively known as
Watt’s law are:
P = I 2R
or
V2
P=
R
8
Power (Example)

What power is dissipated in a 30 Ω resistor through which the
current is 0.125 𝐴?
Solution:
P = IV
P=I R
2
P = (0.125) (30)
2
P = 0.469W
V2
P=
R
P = I 2R
9
Series Circuits
10
Series Circuit
Two elements are in series if:

They have only one terminal in common (i.e., one lead
of one is connected to only one lead of the other).

The common point between the two elements is not
connected to another current-carrying element.
Boylestad L. Robert, 2007, Introductory Circuit Analysis,
10th Edition, Pearson Prentice Hall. Page 130
11
Series Circuit

The current is the same through series elements.

A branch of a circuit is any portion of the circuit that
has one or more elements in series.

The total resistance of a series circuit is the sum of the
resistance levels.
RT = R1 + R2
Boylestad L. Robert, 2007, Introductory Circuit Analysis, 10th Edition,
Pearson Prentice Hall. Page 130
12
Power in Series Circuits

The total power delivered to a resistive circuit is equal to the total
power dissipated by the resistive elements.
PT = P1 + P2

General Equation
RT = R1 + R2 + R3 + ...... + RN
VN
VT V1 V2 V3
= + + + ...... +
I
I
I
I
I
VT = V1 + V2 + V3 + ...... + VN
13
Series Circuit (Example)

Determine total resistance for the circuit of Figure.
𝑅𝑇 = 𝑅1 + 𝑅2 + 𝑅3 + 𝑅4
=7+4+7+7
= 25 Ω
Boylestad L. Robert, 2007, Introductory Circuit Analysis, 10th
Edition, Pearson Prentice Hall. Page 130
14
Series Circuit (Example)

Determine 𝑉2 and 𝐼 for the circuit of Figure.
𝑅𝑇 = 25 Ω
𝐼=
𝐸
50
=
=2𝐴
𝑅𝑇 25
𝑉2 = 𝐼𝑅2 = 2 × 4 = 8 𝑉
Boylestad L. Robert, 2007, Introductory Circuit Analysis, 10th
Edition, Pearson Prentice Hall. Page 130
15
Series Circuit (Example)

Determine 𝑉2 for the circuit of Figure.
𝑅𝑇 = 𝑅1 + 𝑅2 + 𝑅3 = 35 Ω
What if
𝑅2 and 𝑅3
swap location?
𝐼=
𝐸
75
=
= 2.14 𝐴
𝑅𝑇 35
𝑉2 = 𝐼𝑅2 = 2.14 × 5 = 10.7 𝑉
Boylestad L. Robert, 2007, Introductory Circuit Analysis, 10th
Edition, Pearson Prentice Hall. Page 130
16
Series Circuit (Example)

Determine 𝑉2 for the circuit of Figure.
𝑅𝑇 = 𝑅1 + 𝑅2 + 𝑅3 = 35 Ω
𝐼=
𝐸
75
=
= 2.14 𝐴
𝑅𝑇 35
𝑉2 = 𝐼𝑅2 = 2.14 × 5 = 10.7 𝑉
Boylestad L. Robert, 2007, Introductory Circuit Analysis, 10th
Edition, Pearson Prentice Hall. Page 130
17
Interchanging Series Elements

The elements of a series circuit can be interchanged
without affecting the total resistance, current, or
power to each element.
18
Voltage Divider Rule
19
Voltage Divider Rule

Determine 𝑉2 for the circuit of Figure.
𝑅𝑇 = 𝑅1 + 𝑅2 + 𝑅3 = 35 Ω
𝐼=
𝐸
75
=
= 2.14 𝐴
𝑅𝑇 35
𝑉2 = 𝐼𝑅2 = 2.14 × 5 = 10.7 𝑉
We notice:
𝐸
𝑉2 =
𝑅
𝑅𝑇 2
Boylestad L. Robert, 2007, Introductory Circuit Analysis, 10th
Edition, Pearson Prentice Hall. Page 130
𝑅2
𝑉2 =
𝐸
𝑅𝑇
20
Voltage Divider Rule
𝑅𝑥
𝑉𝑥 =
𝐸
𝑅𝑇
𝑅1
𝑉1 =
𝐸
𝑅𝑇
𝑅2
𝑉2 =
𝐸
𝑅𝑇
𝑅𝑇 = 𝑅1 + 𝑅2 + ⋯
21
Voltage Divider Rule
(Example)
Determine the voltage V1 for the network of Figure.
𝑅𝑇 = 20 + 60 = 80 Ω
𝑅1
𝑉1 =
𝐸
𝑅𝑇
𝑉1 =
20
64
80
𝑉1 = 16V
22
Voltage Divider Rule
(Example)

Find voltages across 𝑅1 and 𝑅3 for the circuit of Figure.
𝑅𝑇 = 35 Ω
𝑅1
10
𝑉1 =
𝐸=
75 = 21.4 𝑉
𝑅𝑇
35
𝑉3 =
𝑅3
20
𝐸=
75 = 42.9 𝑉
𝑅𝑇
35
𝑉2 =
𝑅2
5
𝐸=
75 = 10.7 𝑉
𝑅𝑇
35
𝐸 = 𝑉1 + 𝑉3 + 𝑉2 = 75𝑉
Boylestad L. Robert, 2007, Introductory Circuit Analysis, 10th
Edition, Pearson Prentice Hall. Page 130
23
Kirchhoff’s Voltage Law
24
Kirchhoff’s Voltage Law

Kirchhoff’s voltage law (KVL) states that the algebraic sum of the
potential rises and drops around a closed loop (or path) is zero.
V = 0
𝐸 − 𝑉1 − 𝑉2 = 0 or
𝐸 = 𝑉1 + 𝑉2
25
Kirchhoff’s Voltage Law

the applied voltage of a series circuit equals the sum of the voltage
drops across the series elements.

The application of Kirchhoff’s voltage law need not follow a path that
includes current-carrying elements.
V
rise
=Vdrop
𝑉𝑟𝑖𝑠𝑒
𝑉𝑑𝑟𝑜𝑝
−
+
𝑉
𝐼
+
𝑉
𝐼
−
26
Kirchhoff’s voltage Law

Using Kirchhoff’s voltage law, determine the unknown
voltages for the network of Figure.
Σ𝑉𝑟𝑖𝑠𝑒 − Σ𝑉𝑑𝑟𝑜𝑝 = 0
60 − 40 − 𝑉𝑥 + 30 = 0
𝑉𝑥 = 60 − 40 + 30 = 50𝑉
27
Other Notation
28
Double-Subscript Notation

The double-subscript notation Vab specifies point a as
the higher potential. If this is not the case, a negative
sign must be associated with the magnitude of Vab.
In other words,

the voltage Vab is the voltage at point a with respect to
point b.
29
Single-Subscript Notation

The single-subscript notation Va specifies the voltage at
point a with respect to ground (zero volts). If the
voltage is less than zero volts, a negative sign must be
associated with the magnitude of Va .
Va = 10V
Vb = 4V
Vab = Va – Vb
= 10V – 4V
= 6V
30
Double-Subscript Notation
(Example)

Find the voltage Vab for the configuration of Figure
𝑉𝑎𝑏 = 𝑉𝑎 − 𝑉𝑏
= 20 − −15 = 35V
31
Application of Series Circuit
32
Applications

Holiday Lights
Boylestad L. Robert, 2007, Introductory Circuit Analysis,
10th Edition, Pearson Prentice Hall. Page 152
33
Applications
Boylestad L. Robert, 2007, Introductory Circuit Analysis,
10th Edition, Pearson Prentice Hall. Page 153
34
Summary
35
Summary

Ohm’s Law

Energy and Power

Series Circuits

Voltage Divider Rule

Kirchhoff’s Voltage Law

Other Notation

Application of Series Circuit
36
Questions?
Concerns?
e-mail me at
ngjiunnyea@segi.edu.my