Circuit Elements
Circuit element is a mathematical model of a
real device
• Active element: is capable of generating energy
Examples: generators, batteries
• Passive element: absorbs (dissipates) energy
Examples: resistors, capacitors, inductors
Active Element
The most important active elements are voltage
and current sources
• Independent sources
– independent voltage source
– independent current source
• Dependent sources
– dependent voltage source
– dependent current source
Active Element
• Independent voltage source
provides a specified voltage
(independent of the current through the element)
v
+
V
-
1
Active Element
• Independent current source
provides a specified current
(independent of the voltage across the element)
i
Active Element
Dependent source
is a voltage or current generator whose source quantity
depends on another circuit variable (current or voltage)
v
+
-
dependent voltage source
i
dependent current source
Active Element
Dependent source
There are four types of dependent sources:
VCVS, VCCS, CCVS, CCCS
V x: controlling voltage
Ix: controlling current
a,b,c,d: multiplying constants
What are the units?
2
+
-
v=av x
i=cv x
voltage- controlled
voltage source (VCVS)
voltage- controlled
current source (VCCS)
+
-
v = b ix
i = d ix
current- controlled
voltage source (CCVS)
current- controlled
current source (CCCS)
Example
Compute the power that is absorbed or supplied
by the element in the following network.
Ix=4A
Ix
1
2A
+ 12V 2
+
-+
24V
2A
+
3
28V
36 V
-
-
Passive Element
Resistance is the physical ability to resist
current.
The circuit element used to model this behavior
is the resistor.
R
Circuit symbol:
Units for R: Ω
l
A
ρ : resistivit y of the material in O ⋅ m
R=ρ
l : length in m
A : cross - sectional area in m 2
3
Ohm’s Law
• The voltage v across a resistor is directly
proportional to the current I flowing through
the resistor.
v∝i
v = iR
1 O = 1 V/A
R
i
+
v
-
Ohm’s Law
Two possible reference choices for
the current and voltage
+
+
i
i
v
R
-
R
v
v=iR
v=-iR
Conductance
• Conductance is the reciprocal of resistance
G = 1/ R = i / v
Ω
• Symbol: G
• Units: siemens (S) or mho (
)
Example:
Consider a 10 Ω resistor. What is its conductance?
4
Power in a resistor
The power delivered to a resistor is
v
v2
p = vi = v( ) =
R
R
p = vi = (iR)i = i 2 R
R
i
+
v
-
Example
Find
1. G
2. i
vs
3. p(t)
for a. vs=12 V
b. vs=10 cost V
R=1kΩ
i
Model for open and short circuit
(a) A short circuit (R = 0)
(b) An open circuit (R=∞).
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