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Circuit Elements
Ch. 2 – Circuit Elements
2
Basic elements

A passive element is an element which cannot deliver more
energy to the circuit that what is supplied to it by the circuit.
 Resistors, capacitors, inductors are all passive elements

An active element, delivers more energy to the circuit than
what the circuit supplies to it.
 Power sources (i.e. current or voltage sources) are active
elements
ELEC 250 – Summer 2015
Ch. 2 – Circuit Elements
3
Ideal Independent Sources
V
Ideal independent voltage source


It maintains a prescribed voltage across its
terminals regardless of the current through its
terminals
i
i
Ideal independent current source


It maintains a prescribed current through its
terminals regardless of the voltage across its
terminals
V
i
V
Why Ideal Source?
In a real source, the voltage
(current) depends on the current
(voltage) through (across) the
source.

i
V
“real” voltage source
“real” current source
(Internal resistance of the source)
ELEC 250 – Summer 2015
Ch. 2 – Circuit Elements
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Ideal Dependent Sources
(a) Ideal voltage-dependent voltage source
(b) Ideal current-dependent voltage source
(a)
(b)
(c)
(d)
(c) Ideal voltage-dependent current source
(d) Ideal current-dependent current source
Example:
Red Circle: Ideal current-dependent
current source
Blue Circle: Ideal voltage-dependent
voltage source
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Ch. 2 – Circuit Elements
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Example:
Common Emitter Amplifier

You will see it either in
ELEC 330 or ELEC 365

Red Circle: Ideal current-dependent
current source
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Ch. 2 – Circuit Elements
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Allowed or not allowed arrangements
Allowed
Not Allowed
Allowed
Not Allowed
Allowed
Not Allowed
Allowed
ELEC 250 – Summer 2015
Allowed
Not Allowed
Ch. 2 – Circuit Elements
7
Electrical Resistance


Resistance is the capacity of material to impede the
flow of electrical charge (current)
The circuit element that models this behavior is the resistor
Ohm’s Law



v  Ri
The voltage across a resistor is proportional
to the current through the resistor and is
measure in Ohm (Ω)
G  1/ R is the conductance and is measure
in siemens (S).
The sign of the voltage drop across resistor
is determined by the direction of current:
Positive entering, Negative exiting.
ELEC 250 – Summer 2015
or
i  Gv
V
R  tan 

i
Ch. 2 – Circuit Elements
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Example:
v  4i & R  4
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Ch. 2 – Circuit Elements
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Example:
ic
+
va 11 Ω
2.1 A
-
+
-
19 V
3S
(a)
+
3.2 A
id
vb 21 Ω
ELEC 250 – Summer 2015
+
-
12.1 mV 3.3 Ω
Ch. 2 – Circuit Elements
10
Resistor Power
A
Resistor always absorbs power
and is measured in Watt (w).
P = vi
P = Ri 2
 Short Circuit
P=
v
R
2
+
v
-
i
 Open Circuit
R  0 ; V  0 ; i  any value.
R   ; i  0 ; V  any value.
ELEC 250 – Summer 2015
Ch. 2 – Circuit Elements
11
Gustav Kirchhoff
How to Analyze?
Kirchhoff’s Laws
•
•
•
Born 12 March 1812 in Königsberg, Prussia.
Died 17 October 1887 in Berlin
German physicist contributed to electrical
circuits


Kirchhoff’s Current Law (KCL)
Kirchhoff’s Voltage Law (KVL)
ELEC 250 – Summer 2015
Ch. 2 – Circuit Elements

12
Kirchhoff’s Current Law (KCL)
 The sum of currents entering a node equals the sum
of currents leaving the node
 The algebraic sum of all currents at any node in a
circuit equals zero
Examples:
I1  I 2  4
I1  I 2  I3  I 4
I1  I3  I 6  I8
ELEC 250 – Summer 2015
I2  5  2
Ch. 2 – Circuit Elements

13
Kirchhoff’s Voltage Law (KVL)
 The algebraic sum of all the voltages around any
closed path in a circuit equals zero
 The sum of voltage rise around a loop equals the
sum of drop around the same loop
Examples:
V1
For each loop, we can write a KVL
(a)  v1  v2  v4  vb  v3  0
(b)  va  v3  v5  0
V2
5v
(c) vb  v4  vc  v6  v5  0
(d)  v1  v2  vc  v7  vd  va  0
V3
5  V1  V2  V3  0
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Ch. 2 – Circuit Elements
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Examples:
The circuits with independent sources
The circuits with dependent sources
(c)
(a)
(b)
(d)
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Ch. 2 – Circuit Elements
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Example (a) - Solution:
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Ch. 2 – Circuit Elements
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Example (b) - Solution:
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Ch. 2 – Circuit Elements
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Example (c) - Solution:
i
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Ch. 2 – Circuit Elements
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Example (d) - Solution:
ig
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Ch. 2 – Circuit Elements
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Examples for Tutorial:
The circuit with independent sources
The circuits with dependent sources
(b)
(a)
(c)
ELEC 250 – Summer 2015