Chapter 2
Engr228
Circuit Analysis
Dr Curtis Nelson
Chapter 2 Objectives
•  Understand the symbols for and the behavior of the following
ideal basic circuit elements:
–  Independent voltage and current sources
–  Dependent voltage and current sources
–  Resistors
•  Be able to state Ohm’s law, Kirchhoff’s current and voltage
laws, and be able to use these laws to analyze simple circuits.
•  Know how to calculate the power for each element in a simple
circuit and be able to determine whether or not the power
balances for the whole circuit.
Circuit Element Review
•  A circuit element most often has
two terminals.
•  The relationship between the
voltage v across the terminals and
the current i through the device
defines the circuit element model.
Various Circuit Elements
•  Electric sources
–  Independent Sources – voltage, current
–  Dependent Sources – voltage, current
•  Resistors, inductors, capacitors
•  Measurement devices
–  Ammeters (current)
–  Voltmeters (volt)
–  Ohmmeters (resistance)
•  Electric wire
Independent Voltage Sources
•  An ideal voltage source is a circuit element that will maintain
the specified voltage vs across its terminals.
•  The current will be determined by other circuit elements.
A Battery as an Independent Voltage Source
•  A voltage source is an ideal version of a battery in that a battery
is supposed to provide a constant “dc” voltage, V, but in
practice a battery has a maximum power that it can deliver.
Independent Current Sources
•  An ideal current source is a circuit element that maintains the
specified current flow is through its terminals.
•  The voltage is determined by other circuit elements.
Dependent Voltage and Current Sources
•  A dependent voltage or current
source establishes a voltage or
current whose value depends on a
voltage or current elsewhere in
the circuit.
•  You cannot specify the value of a
dependent source unless you
know the value of the voltage or
current on which it depends.
•  Dependent sources are sometimes
called controlled sources.
Active and Passive Elements
•  Active elements are physical elements that are capable of
generating electric energy:
–  Voltage sources
–  Current sources
•  Passive elements are physical elements that cannot generate
electric energy:
– 
– 
– 
– 
Resistors
Capacitors
Inductors
Transistors
Interconnections of Ideal Sources
•  Which of the following are valid connections?
a)
b)
c)
d)
e)
Valid
Valid
Not Valid
Not Valid
Valid
The Concept of Ground
•  Ground is commonly referred to as a reference point.
•  Ground, by convention, is said to be at a potential of 0.00
volts. In other words, Ground has zero voltage.
•  Ground symbols:
Ground
1 Volt
1V
1Ω
0 Volts
Open and Short Circuits
•  An open circuit means no
current can flow (i = 0).
•  Voltage across an open
circuit: any value.
•  An open circuit is equivalent
to a resistance of ∞ Ω.
•  Open circuit: infinite
resistance, current must be
zero, voltage can be any
value.
1V
1Ω
Short Circuit vs. Open Circuit
•  A short circuit means that
the voltage is zero (v = 0).
•  Current through a short
circuit: any value.
•  A short circuit is equivalent
to a resistance of 0 Ω.
•  Short circuit: zero
resistance, voltage across
must be zero, current can be
any value.
1V
1Ω
Current Flow
•  Every element in the circuit below has a current = 1A
1A
1V
1Ω
1A
1A
Voltage (Potential)
•  Every element in the circuit below has a voltage across it of 1V
x + 1 Volts
1V
1Ω
x Volts
Resistance (R) and Conductance (G)
•  Resistance (R) is the capacity of a material to impede the
flow of current.
•  Conductance (G) is the inverse of resistance.
•  More current will flow if there is less resistance, or more
conductance.
•  The unit of resistance is the ohm (R), has the symbol Ω, and
units of (volts/amp).
•  The unit of conductance is siemens (S), has an upside-down
ohms symbol, and units of (amps/volt).
•  The circuit symbol used for a resistor of R ohms is:
Ohm’s Law
•  The relationship between voltage, current, and resistance is
defined by Ohm’s law which states that
V = IR
where
V = the voltage in volts;
I = the current in amps;
R = the resistance in ohms.
Other Forms of Ohm’s Law
•  Ohm’s law can be expressed in any one of three forms,
depending on which quantities are known:
V = IR
I = V/R
R = V/I
Example 2.3 - Nilsson 9th
Calculate the values of v and i in the examples below. Also,
determine the power dissipated in each resistor.
a) 
b) 
c) 
d) 
va = 8V
ib = 10A
vc = -20V
id = -2A
p = 8W
p = 500W
p = 20W (positive)
p = 100W
Ohm’s Law Illustrated
Wire Gauge and Resistivity
•  The resistance of a wire is determined by the resistivity of the
conductor as well as the geometry:
R=ρl/A
•  In most cases, the resistance of wires can be assumed to be 0 Ω.
Resistors
Resistor Color Code Chart
Ohm’s Law Example
Calculate the value of R from the information shown in the
graph below.
R is the inverse of the slope of the line:
R = V/I = (8V)/(4A) = 2Ω
Power and its Alternative Forms
Resistors absorb power: since v = iR
p = vi = v2/R = i2R
Positive power means the element is absorbing energy.
Power is always positive for a resistor.
Power Example
Calculate the power absorbed or generated by each element in
the circuit below:
2.5mA
10V
4KΩ
•  DC source generates power = 10V * -2.5mA = - 25mW
•  Resistor absorbs power = 10V * 2.5mA = 25mW
Resistors always absorb power but DC sources can either
generate or absorb power.
Nodes, Paths, Loops, Branches
•  These two networks are equivalent
•  There are three nodes and five branches
–  Node: a point at which two or more elements have a common connection
point
–  Branch: a single path in a network composed of one simple element and
the node at each end of that element
•  A path is a sequence of nodes
•  A loop is a closed path
Kirchhoff’s Current Law
•  Kirchhoff’s Current Law (KCL) states that the algebraic sum
of all currents entering a node is zero.
iA + iB + (−iC) + (−iD) = 0
KCL: Alternative Forms
•  Current IN is zero:
iA + iB + (−iC) + (−iD) = 0
•  Current OUT is zero:
(-iA )+ (-iB ) + iC + iD = 0
•  Current IN = Current OUT:
iA+ iB = iC + iD
Example of KCL Application
Find the current through resistor R3 if it is known that the voltage
source supplies a current of 3 A.
Answer: i =6 A
Kirchhoff’s Voltage Law
•  Kirchhoff’s Voltage Law (KVL) states that the algebraic sum
of the voltages around any closed path is zero.
-v1 + v2 + -v3 = 0
KVL: Alternative Forms
•  Sum of RISES is zero (clockwise from B):
v1 +(- v2 ) + v3 = 0
•  Sum of DROPS is zero (clockwise from B):
(-v1 ) + v2 + (-v3 ) = 0
•  Sum of RISES is equal to sum of DROPS (clockwise from B):
v1 + v2 = v3
Applying KVL
Find the current ix and the voltage vx
Answer: vx= 12 V and ix =120 mA
Textbook Problem 2.19 (Nilsson 9E)
Find the values of ia, ib, vo, and the power absorbed or generated
by all circuit elements.
ia = 2A
ib = 0.5A
vo = 40V
P4 = 25W
P20 = 80W
P80 = 20W
P50v = -125W (delivered)
Circuit Analysis with Dependent Sources
•  Circuits that contain dependent sources can be analyzed using
Ohm’s and Kirchhoff’s laws.
•  A dependent source generally adds another equation to the
solution process.
Textbook Example - Figure 2.22 (Nilsson 9E)
A)  Use Kirchhoff’s laws and Ohm’s law to find the voltage vo
as shown below.
B)  Show that the total power developed equals the total power
dissipated.
A) vo = 480 V
B) Power developed = - 21.7 W
Example
Compute the power absorbed in each element of the circuit below:
+ -
30Ω
120V
Answer: P120 =
P30 =
Pdep =
P15 =
-960W
1920W
-1920W
960W
2VA
15Ω
VA
+
Chapter 2 Summary
•  Defined the symbols for and the behavior of the following
ideal basic circuit elements:
–  Independent voltage and current sources;
–  Dependent voltage and current sources;
–  Resistors.
•  Defined and illustrated Ohm’s law, Kirchhoff’s current and
voltage laws, and how to use these laws to analyze simple
circuits.
•  Explained how to calculate the power for each element in a
simple circuit and be able to determine whether or not the
power balances for the whole circuit.