03-Circuit Elements
Text: Chapter 1.6 – 1.9, 2.3
ECEGR 210
Electrical Circuits I
Overview
• Circuit Topology
• Series and Parallel Connections
• Sources
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Circuit Topology
• Circuits are usually described graphically
• Need to be proficient in understanding basic
circuit symbols
• Road map:
 Circuit topology (branches, nodes, loops)
 Active elements
 Passive elements (later lectures)
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Branch
• Branch: a single element in a network
 Examples: single voltage source, resistor
 Orientation does not matter
 Terminals are part of the branch
• Example below has five branches
branch
branch
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Node
• Node: point of common connection between two
or more branches
• Example below has three nodes
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Loops
• Loop: any closed path in a network
• Start at a node, pass through at least one other
node and return to the original node
 Direction matters
• Independent loop: a loop that contains at least
one branch not contained in another loop
 Independent loops have independent equations
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Topology Relations
• For all networks
 B = L + N -1
• Where
 B = number of branches
 L = number of loops
 N = number of nodes
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Series Connections
• Two branches (elements) are in series if they
exclusively share a single node
• Same current flows through each element
• Network below:
 A and B are in series
 No other elements are in series
B
A
C
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D
E
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Parallel Connections
• Two branches (elements) are in series if they
share both nodes
• Network below:
 C, D, E are in parallel
• It is possible for two elements to not be in series
or in parallel (e.g. B and C)
B
A
C
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D
E
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Example
• Which elements are in series?
D
B
A
C
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E
F
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Example
• Which elements are in series?
 A, B
 D, E, F
D
B
A
C
E
F
C prevents B and D from being in series
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Example
• Which elements are in parallel?
D
B
A
C
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E
F
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Example
• Which elements are in parallel?
 None
 But C is in parallel if D, E and F can be combined
into a single element G (more on this later)
D
B
A
C
E
G
B
F
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A
C
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Circuit Elements
• Two types of elements:
 Active: supplies energy
• Batteries, generators, etc
 Passive: cannot supply energy (may or may not
consume energy)
• Resistors, inductors, capacitors
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Voltage and Current Sources
• We are concerned with ideal voltage and current
sources
• Voltage source: prescribed voltage, can supply
infinite current with no loss
• Current source: prescribed current, can supply
infinite voltage with no loss
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Voltage and Current Sources
• V-I characteristics
Ideal voltage source
current
voltage
Ideal current source
current
voltage
Examples of non-ideal sources
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Voltage/Current Sources
• Current and voltage sources are active elements
• Two types:
 Independent (I or V are independent from other
circuit elements)
 Dependent: (I or V depend on other circuit
elements)
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Independent/Dependent Sources
Current
Voltage
Dependent
+
-
+
Independent
-
DC
DC
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Dependent Sources
• Dependent Voltage Sources:
 Often controlled by voltage or current in the circuit
 Generators voltage controlled by rotational speed
• Dependent Current Sources:
 Often controlled by voltage or current in the circuit
V
+
-
i
C
B
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+
A
-
10i
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Example
• Find the power consumed or supplied by each
element
I=5A
20V
+
-
+ 12V -
6A
+
8V
-
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0.2I
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Example
• Find the power consumed or supplied by each
element




20 x -5 = -100W (supply)
12 x 5 = 60 W
6 x 8 = 48W
-0.2x5 x 8 = -8 W(supply)
I=5A
+ 12V 60W
20V
-100W
+
-
+
6A 48W 8V
-
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0.2I
-8W
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Sources
• Voltage sources can be easily conceptualized as a
battery
• What about current sources?
 One example is in the internal model of a
photovoltaic cell
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