Basic Electric Circuits Session 2

Basic Electric Circuits – © 2020 Mouli Sankaran Email: mouli.sankaran@yahoo.com 2
Session 2: Focus
 Simple Circuit Elements
 Independent Voltage Sources
 Independent Current Sources
 Dependent Voltage Sources
◦ Voltage-controlled voltage source
◦ Current-controlled voltage source
 Dependent Current Sources
◦ Current-controlled current source
◦ Voltage-controlled current source
 Solving example problems
 Home Work Problems

Simple Circuit Elements

Simple Circuit Elements Definition
 A simple circuit element is the mathematical model
of a two-terminal electrical device
 Particular model of a real device is derived based on
the experimental data or experience
 Circuit elements are completely characterized by its
voltage-current relationship
 It cannot be subdivided further into other two-
terminal devices

Independent Voltage Sources

Independent Voltage Source
 An independent voltage source is characterized by a
terminal voltage which is completely independent of
the current through it
◦ Or current or power supplied by it
 The independent voltage source is an ideal source and
it does not represent exactly any real physical device
Whatever be
the current
drawn from the
voltage source,
the voltage (V0)
supplied by the
source remains
the same
V0
V0
V0 =
v
i

Various Independent Voltage Sources
 (a): DC Voltage source symbol
 (b): Battery symbol
 (c): AC Voltage source symbol

Independent Current Sources

Independent Current Source
 An independent current source is characterized by a
terminal current which is completely independent of
the voltage across it
 The independent current source is an ideal source and
does not represent exactly any real physical device
Whatever be
the voltage
across the
current source,
the current (I0)
supplied by the
source remains
the same
I0
I0 =
v
i

Voltage across Independent Current Sources
 It is a common mistake to view an independent
current source as having zero voltage across its
terminals while providing a fixed current
 In fact, we do not know a priori what the voltage
across a current source will be
◦ It depends entirely on the circuit to which it is connected.
Caution!!

Use of Mobile Battery
Supplying or absorbing?Supplying or absorbing?
SupplyingAbsorbing

Independent Sources –
Normally Supply Power
 In their normal mode of operation, independent
sources supply power to the remainder of the circuit.
 However, independent sources may also be
connected into a circuit in such a way that they
absorb power
◦ An example of this is a cell phone battery being connected
to a battery-charging circuit
◦ While the battery is getting charged, it absorbs power from
the charging circuit
◦ After getting charged, when the mobile is functioning
normally, it will be supplying power to the phone

Dependent Sources

Dependent Sources
 In contrast to the independent sources, which produce a
particular voltage or current completely unaffected by
what is happening in the remainder of the circuit
 Dependent sources generate a voltage or current that is
determined by a voltage or current at a specified location
in the circuit
 These sources are very important because they model
the behaviour of many electronic circuit elements

Dependent Voltage Sources
 (a): Voltage-controlled voltage source
 (b): Current-controlled voltage source
Note: Where K and r are some dimensionless scaling constants
(a) (b)

Example 1: Dependent Voltage Source
 Which one is a dependent source here?
 What is the type of Dependent source shown on the
top right of the circuit?
 Voltage-controlled voltage source
◦ Depends on the voltage Vx in the circuit, value of K here is 2

Example 2: Dependent Voltage Source
right?
 Current-controlled voltage source
◦ Depends on the current Ix in the circuit, value of K here is 4

Dependent Current Sources
 (a): Current-controlled current source
 (b): Voltage-controlled current source
Note: Where K and g are dimensionless scaling constants
(a) (b)

Example 3: Dependent Current Source
right of the circuit?
 Current-controlled current source
◦ Depends on the current Ix in the circuit, value of K here is 2
- +

Example 4: Dependent Current Source
right of the circuit?
 Voltage-controlled current source
◦ Depends on the voltage vx in the circuit, value of K here is 0.25

About Dependent Sources
 As a circle is used to represent independent sources,
a diamond is used to represent dependent sources
◦ They are called as a dependent or controlled sources
 A voltage source which depends on the voltage at
some other part of the circuit may appear strange
 But such sources are invaluable to model many
electronic circuits

Solving Example Problems

Example 1: Solution
 Compute the power supplied or absorbed by the
element 1.
◦ Voltage across the element 1 =
◦ Current through the element 1 =
◦ Does the current enter through +ve or –ve terminal of
◦ element 1?
◦ Power absorbed by the element 1 = p = v * I = 4 * 2 =
+ve terminal
Note: This problem is P 1.34 on
page 22, Figure P 1.34 in the Ref 2
book (by Irwin)
4 V
2 A
8 W

Example 2: Solution
Note: This problem is E 1.5
on page 12, Figure E 1.5 in
the Ref 2 book (by Irwin)
 Compute the power supplied or absorbed by the
element 1.
◦ Voltage across the element 1 =
◦ Current through the element 1 =
◦ Does the current enter through +ve or –ve terminal of
◦ element 1?
◦ Power absorbed by the element 1 = p = v * I = 4 * 8=
+ve terminal
8 V
4 A
32 W

Example 3: Solution
 Compute the power supplied by Element 1.
◦ Total power supplied = P18V + P1 + P24V
◦ = - (18 Ix) – (6 Ix) – (24*2) = -24 Ix - 48
◦ Total power absorbed = P2 + P2Ix
◦ = 4* (2 Ix) + 20 * (2 Ix) = 48 Ix
◦ Total power supplied + Total power absorbed = 0
◦ -24 Ix – 48 + 48Ix= 0
◦ 48 = 24 Ix
◦ Ix = 2 A
= 8 A
Result:
Power supplied by
Element 1 = 6 * Ix
= - (6 * 2)
= -12W
20 V
- +
Conservation of
Energy
Note: This problem is P 1.37 on page 23, Figure P
1.37 in the Ref 2 book (by Irwin)

Example 4: Solution
 Find the power absorbed or supplied by each element.
(left to right)
 P7A = - 8 * 7 = -56 W
 P1 = 8 * 2 = 16 W
 P2 = - 12 * 5 = -60 W
 P3 = 20 * 8 = 160 W
 -vx = 12 V
 vx = -12 V
 P0.25vx = 20 * (0.25vx)
 = 20 * 0.25 * (-12)
 = - 60W
+
-
Current
= -3A
Voltage
= 20 V
Note: This problem is Practice 2.9 on page 20, Figure 2.20 in the Ref 1 book (by Hayt)
2
31

Home Work Problems

S2_HW_Problem_1
 Find the power absorbed or supplied by the elements.
 P20V:
 P1:
 P14V:
-40 W supplied
12 W absorbed
28 W absorbed
Note: This problem is P 1.31 (a) on page 22, Figure P 1.31 in the Ref 2 book (by Irwin)

S2_HW_Problem_2
 Find the power absorbed or supplied by the elements.
 P4A:
 P1:
 P2Ix :
-64 W supplied
32 W absorbed
32 W absorbed
Note: This problem is P 1.31 (b) on page 22, Figure P 1.31 in the Ref 2 book (by Irwin)

S2_HW_Problem_3
 Find the unknown power absorbed by Element 1.
 Ix:
 P1:
2 A
24 W
Note: This problem is P 1.36 on page 23, Figure P 1.36 in the Ref 2 book (by Irwin)
Clue: Compute the power supplied or power
Absorbed by each element.
The power supplied will be–ve and
Power absorbed values will be +ve.
Adding them and equating them to zero.
Solve the equation to find Ix. Then compute P1.

S2_HW_Problem_4
 Find the power supplied/absorbed by the each
elements in the circuit.
Note: This problem is Exercise 29 on page 33, Figure 2.31 in the Ref 1 book (by Hayt)
P2V :-4 W
P3A : 30 W
P4A :40 W
P10V : -50 WP8V :-16 W

S2_HW_Problem_5
 Find the power absorbed by each element.
 Given: VR = 10V and Vx = 2V
 5Vx :
 PAVx :
 PA :
 P5Vx :
10A
Note: This problem is Exercise 33 on page 33, Figure 2.33 in the Ref 1 book (by Hayt)
-20 W
100 W
-80 W

Session 2: Summary
 Simple Circuit Elements
 Independent Voltage Sources
 Independent Current Sources
 Dependent Voltage Sources
◦ Voltage-controlled voltage source
◦ Current-controlled voltage source
 Dependent Current Sources
◦ Current-controlled current source
◦ Voltage-controlled current source
 Solving example problems
 Home Work Problems

References
Ref 1 Ref 2

Basic Electric Circuits Session 2

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