Introduction to Circuit Analysis- Basic Concepts Fundamentals of Electric Circuits

1. 1
Fundamentals of Electric CircuitsFundamentals of Electric Circuits
Chapter 1Chapter 1
Basic ConceptsBasic Concepts

2. 2
Basic Concepts - Chapter 1Basic Concepts - Chapter 1
1.1 Systems of Units.
1.2 Electric Charge.
1.3 Current.
1.4 Voltage.
1.5 Power and Energy.
1.6 Circuit Elements.

3. 3
1.1 System of Units (1)1.1 System of Units (1)
Quantity Basic unit Symbol
Length meter m
Mass kilogram Kg
Time second s
Electric current ampere A
Thermodynamic
temperature
kelvin K
Luminous intensity candela cd
Six basic units

4. 4
1.1 System of Units (2)1.1 System of Units (2)
The derived units commonly used in electric circuit theory
Decimal multiples and
submultiples of SI units

5. 5
1.2 Electric Charges1.2 Electric Charges
• Charge is an electrical property of the atomic
particles of which matter consists, measured in
coulombs (C).
• The charge e on one electron is negative and
equal in magnitude to 1.602 × 10-19
C which is
called as electronic charge. The charges that
occur in nature are integral multiples of the
electronic charge.

6. Cont…Cont…
1. The coulomb is a large unit for charges. In 1 C of
charge, there are 1/(1.602 × 10−19) = 6.24 × 10^18
electrons. Thus realistic or laboratory values of
charges are on the order of pC, nC, or μC
2. According to experimental observations, the only
charges that occur in nature are integral multiples of
the electronic charge e = −1.602 × 10−19 C.
3. The law of conservation of charge states that charge
can neither be created nor destroyed, only
transferred. Thus the algebraic sum of the electric
charges in a system does not change.
6

7. 7
1.3 Current (1)1.3 Current (1)

8. Types of CurrentTypes of Current
• If the current does not change with time, but remains
constant, we call it a direct current (dc).
• A direct current (dc) is a current that remains constant with
time.
• A time-varying current is represented by the symbol i.
• A common form of time-varying current is the sinusoidal
current or alternating current (ac).
• An alternating current (ac) is a current that varies
sinusoidally with time.
8

9. 9
1.3 Current (2)1.3 Current (2)
• The direction of current flow
Positive ions Negative ions

10. 10
1.3 Current (3)1.3 Current (3)
Example 1
A conductor has a constant current of
5 A.
How many electrons pass a fixed point
on the conductor in one minute?

11. 11
1.3 Current (4)1.3 Current (4)
Solution
Total no. of charges pass in 1 min is given by
5 A = (5 C/s)(60 s/min) = 300 C/min
Total no. of electronics pass in 1 min is given
minelectrons/1087.1
C/electron10602.1
C/min300 21
19
x
x
=−

12. 12
1.4 Voltage (1)1.4 Voltage (1)
• Voltage (or potential difference) is the energy
required to move a unit charge through an
element, measured in volts (V).
• Mathematically, (volt)
– w is energy in joules (J) and q is charge in coulomb (C).
• Electric voltage, vab, is always across the circuit
element or between two points in a circuit.
– vab > 0 means the potential of a is higher than potential of
b.
– vab < 0 means the potential of a is lower than potential of
b.
dqdwvab /=

13. Cont…Cont…
• Current and voltage are the two basic variables in electric
circuits.
• The common term signal is used for an electric quantity
such as a current or a voltage (or even electromagnetic
wave) when it is used for conveying information.
• Engineers prefer to call such variables signals rather than
mathematical functions of time because of their importance
in communications and other disciplines.
• Like electric current, a constant voltage is called a dc
voltage and is represented by V, whereas a sinusoidally
time-varying voltage is called an ac voltage and is
represented by v.
• A dc voltage is commonly produced by a battery; ac
voltage is produced by an electric generator.
13

14. 14
1.5 Power and Energy (1)1.5 Power and Energy (1)
• Power is the time rate of expending or absorbing
energy, measured in watts (W).
• Mathematical expression: vi
dt
dq
dq
dw
dt
dw
p =⋅==
i
+
–
v
i
+
–
v
Passive sign convention
P = +vi p = –vi
absorbing power supplying power

15. Cont…Cont…
• The power p in Eq.(Previous) is a time-varying quantity and
is called the instantaneous power.
• Thus, the power absorbed or supplied by an element is the
product of the voltage across the element and the current
through it.
• If the power has a + sign, power is being delivered to or
absorbed by the element.
• If, on the other hand, the power has a − sign, power is
being supplied by the element. But how do we know when
the power has a negative or a positive sign?
• Passive sign convention is satisfied when the current enters
through the positive terminal of an element and p = +vi. If
the current enters through the negative terminal, p = −vi.
15

16. Cont…Cont…
• Unless otherwise stated, we will follow the passive sign
convention throughout this text.
• For example, the element in both circuits of Fig. 1.9 has an
absorbing power of +12 W because a positive current
enters the positive terminal in both cases.
• In Fig. 1.10, however, the element is supplying power of
−12W because a positive current enters the negative
terminal.
• Of course, an absorbing power of +12 W is equivalent to a
supplying power of −12 W. In general,
+ Power absorbed = −Power supplied
• In fact, the law of conservation of energy must be obeyed
in any electric circuit. For this reason, the algebraic sum of
power in a circuit, at any instant of time, must be zero:
16

17. Cont…Cont…
17
a.P=4x3=12a.P=4x3=12
b.P=4x3=12b.P=4x3=12
c.P=4x(-3)=-12c.P=4x(-3)=-12
d.P=4x(-3)=-12d.P=4x(-3)=-12

18. 18
1.5 Power and Energy (2)1.5 Power and Energy (2)
• The law of conservation of energy
∑ = 0p
• Energy is the capacity to do work, measured
in joules (J).
• Mathematical expression ∫ ∫==
t
t
t
t
vidtpdtw
0 0

19. 1.6 Circuit Elements1.6 Circuit Elements
• There are two types of elements found in electric circuits:
passive elements and active elements.
• An active element is capable of generating energy while a
passive element is not.
• Examples of passive elements are resistors, capacitors, and
inductors.
• Typical active elements include generators, batteries, and
operational amplifiers.
• Our aim in this section is to gain familiarity with some
important active elements.
• The most important active elements are voltage or current
sources that generally deliver power to the circuit
connected to them.
• There are two kinds of sources: independent and
dependent sources. 19

20. 20
1.6 Circuit Elements (1)1.6 Circuit Elements (1)
Active Elements Passive Elements
Independent
sources
Dependant
sources
• A dependent source is an active
element in which the source quantity
is controlled by another voltage or
current.
• They have four different types: VCVS,
CCVS, VCCS, CCCS. Keep in minds the
signs of dependent sources.

21. Voltage SourceVoltage Source
• An ideal independent source is an active element that
provides a specified voltage or current that is completely
independent of other circuit variables.
• An ideal independent voltage source delivers to the circuit
whatever current is necessary to maintain its terminal
voltage.
• Physical sources such as batteries and generators may be
regarded as approximations to ideal voltage sources.
• Symbols for independent voltage sources:
• Used for constant or time-varying voltage.
• Used for constant voltage (dc).
21

22. Current SourceCurrent Source
• An ideal dependent (or controlled) source is an active
element in which the source quantity is controlled by
another voltage or current.
• An ideal independent current source is an active element
that provides a specified current completely independent of
the voltage across the source.
• That is, the current source delivers to the circuit whatever
voltage is necessary to maintain the designated current.
• Dependent sources are usually designated by diamond-
shaped symbols, as shown in Fig.
• Symbols for:
• Dependent voltage source.
• Dependent current source.
22

23. Cont…Cont…
• Since the control of the dependent source is achieved by a
voltage or current of some other element in the circuit, and
the source can be voltage or current,
• It follows that there are four possible types of dependent
sources, namely:
1. A voltage-controlled voltage source (VCVS).
2. A current-controlled voltage source (CCVS).
3. A voltage-controlled current source (VCCS).
4. A current-controlled current source (CCCS).
• Dependent sources are useful in modeling elements such as
transistors, operational amplifiers and integrated circuits.
23

24. Cont…Cont…
• An example of a current controlled voltage source is shown
on the right-hand side of Fig. 1.14, where the voltage 10i
of the voltage source depends on the current i through
element C.
• Students might be surprised that the value of the
dependent voltage source is 10i V (and not 10i A) because
it is a voltage source.
• The key idea to keep in mind is that a voltage source
comes with polarities (+ −) in its symbol, while a current
source comes with an arrow, irrespective of what it
depends on. 24

25. Cont…Cont…
• It should be noted that an ideal voltage source (dependent
or independent) will produce any current required to ensure
that the terminal voltage is as stated, whereas an ideal
current source will produce the necessary voltage to ensure
the stated current flow.
• Thus an ideal source could in theory supply an infinite
amount of energy.
• It should also be noted that not only do sources supply
power to a circuit, they can absorb power from a circuit
too.
• For a voltage source, we know the voltage but not the
current supplied or drawn by it.
• By the same token, we know the current supplied by a
current source but not the voltage across it.
25

26. 26
1.6 Circuit Elements (2)1.6 Circuit Elements (2)
Example 2
Obtain the voltage v in the branch shown in Figure 2.1.1P for i2
= 1A.
Figure 2.1.1P

27. 27
1.6 Circuit Elements (3)1.6 Circuit Elements (3)
Solution
Voltage v is the sum of the current-independent
10-V source and the current-dependent voltage
source vx.
Note that the factor 15 multiplying the control
current carries the units Ω.
Therefore, v = 10 + vx = 10 + 15(1) = 25 V