Mesh and nodal

1. DIFFERENT ENERGY
SOURCES

2. V,I,R
 Voltage is the difference in charge between two
points.
 Current is the rate at which charge is flowing.
 Resistance is a material’s tendency to resist the
flow of charge (current).

3. ELECTRIC POWER
 Electric power is the rate of energy consumption
in an electrical circuit.
 The electric power is measured in units of watts.
 P is the electric power in watt (W).
 E is the energy consumption in joule (J).
 t is the time in seconds (s).

4. ACTIVE AND PASSIVE ELEMENTS
 Active electronic components are those that can
control the flow of electricity. Most
electronic printed circuit boards have at least one
active component. Some examples of active
electronic components are transistors, vacuum
tubes, silicon-controlled rectifiers (SCRs).
 Passive electronic components are those that
don’t have the ability to control current by means
of another electrical signal. Examples of passive
electronic components are capacitors, resistors,
inductors, transformers, and diodes.

5. OHM’S LAW
 Ohm's Law states that the current flowing in a
circuit is directly proportional to the applied
potential difference and inversely proportional to
the resistance in the circuit under constant
physical conditions.
 V=IR
Where:
V = voltage expressed in Volts
I = current expressed in Amps
R = resistance expressed in Ohms

6. CURRENT DIVISION RULE
 Current division refers to the splitting of
current between the branches of the divider. The
currents in the various branches of such a circuit
will always divide in such a way as to minimize
the total energy expended.

7.  A general formula for the current IX in a
resistor RX that is in parallel with a combination
of other resistors of total resistance RT is:
 where IT is the total current entering the
combined network of RX in parallel with RT.
Notice that when RT is composed of a parallel
combination of resistors, say R1, R2, ... etc., then
the reciprocal of each resistor must be added to
find the total resistance RT:

8. VOLTAGE DIVISION RULE
 Voltage Division Rule: The voltage is divided between
two series resistors in direct proportion to their
resistance.

9.  Results

10. USE OF CALCULATORS,

12. DEPENDENT AND INDEPENDENT SOURCES

14. IDEAL AND NON-IDEAL ENERGY SOURCES
 An Ideal voltage source is a voltage source
that maintains the constant Voltage across its
terminals no matter how much current is drawn
from it.
An ideal Voltage soure will have Zero
internal resistance.
 An ideal current source is a current source in
which can supply constant current regardless of
any voltage drops in the circuit.
The ideal current source will have infinite
internal resistance.

16. IDEAL VOLTAGE SOURCE

17. IDEAL CURRENT SOURCE

18.  Non Ideal voltage source have some internal
resistance in series. Whenever load connected
some drop of voltage observed.
 Non ideal current source have some internal
resistance in parallel.
Whenever load connected current will be slightly
less than the rated constant value.

19. PRACTICAL VOLTAGE SOURCE

20. PRACTICAL CURRENT SOURCE

21. EXAMPLE 1
 A Lithium-Ion (Li-Ion) battery pack for a
camcorder is rated as 7.2 V and 5 W-hours. What
are its equivalent ratings in mA-hours and
joules?
 Since a joule( J ) is equivalent to a W-second, 5
W-hours is the same as 5 × 3600 =18000 J.
Since the battery has a voltage of 7.2 V, the battery
rating in ampere-hours is 5/7.2 =0.69.
Equivalently, its rating in mA-hours is 690.

22. EXAMPLE 2
 Does a Nickel-Cadmium(Ni-Cad) battery pack
rated at 6 V and 950 mA-hours store more or less
energy than a Li-Ion battery pack rated at 7.2 V
and 900 mA-hours?
 We can directly compare the two by converting
their respective energies into joules. The Ni-Cad
battery pack stores 6 × 950 × 3600/1000 = 20520
J, while the Li-Ion battery pack stores 7.2 × 900
× 3600/1000 = 23328 J. Thus the Li-Ion battery
pack stores more energy.

23. EXAMPLE 3
Determine the resistance of a cube with sides of
length 1 cm and resistivity 10 ohm-cms, when a
pair of opposite surfaces are chosen as the
terminals.
 Substituting ρ = 10 ohm-cm, l = 1 cm, w = 1 cm,
and h = 1 cm, we get
 R = 10 ohm.

24. EXAMPLE 4
 By what factor is the resistance of a wire with
cross-sectional radius r greater than the
resistance of a wire with cross-sectional radius
2r?
 A wire is cylindrical in shape. Equation 1.5
relates the resistance of a cylinder to its cross-
sectional area. Rewriting Equation in terms of
the cross-sectional radius r
we have
 From this equation it is clear that the resistance
of a wire with radius r is four times greater than
that of a wire with cross-sectional radius 2r.

25. DEPENDENT SOURCES
 A dependent source is either a voltage source or
current source whose value depends upon a
voltage or current value somewhere else in the
circuit. These are of four types depending on the
controlling variable and output of the source.
1. VCVS
2. VCCS
3. CCVS
4. CCCS

26. VOLTAGE CONTROLLED VOLTAGE SOURCES:
 This is a voltage source whose output can be controlled
by changing the controlling voltage .

27. VOLTAGE CONTROLLED CURRENT SOURCES:
 In case the control variable is voltage and the output of
the source is current, it is VCCS.

28. CURRENT CONTROLLED CURRENT SOURCE
 The source delivers the current as per the current
of the dependent element.

29. CURRENT CONTROLLED VOLTAGE SOURCE
 The source delivers the voltage as per the current
of the dependent element.

31. LINEAR AND NON LINEAR ELEMENTS
 Linear elements – In an electric circuit, a linear
element is an electrical element with
a linear relationship between input current and
output voltage. The resistance, inductance or
capacitance offered by an element does not change with
the change in applied voltage or circuit current, the
element is termed as linear element. Resistors are the
most common example of a linear element; other
examples include capacitors, inductors,
and transformers.

32. NONLINEAR ELEMENTS
 In an electric circuit, a nonlinear element or nonlinear
device is an electrical element which does not have
a linear relationship between current and voltage.
A diode is a simple example. The current I through a
diode is a non-linear function of the voltage V across its
terminals:
 Other examples of nonlinear elements
are transistors and
other semiconductor devices, vacuum tubes, and iron
core inductors and transformers when operated above
their saturation current.

34. BASICS OF DC
 Concept of notations :
 We adopt the convention that a constant or direct
current (DC) or voltage is represented by an upper-case
letter I or V, while a time-varying or alternating current
(AC) current or voltage is represented by a lower-case
letter i(t) or v(t), sometimes simply i and v.
 Each of the three basic components resistor R, capacitor
C, and inductor L can be described in terms of the
relationship between the voltage across and the current
through the component:


35. RESISTOR
 The voltage across and the current through a resistor
are related by Ohm's law:
 Here R is the resistance of the conductor measured by
Ohm.
 The reciprocal of the resistance is the conductance:

 Conductance is measured Siemens = 1/Ohm by S.

36. CAPACITOR
 A capacitor is composed of a pair of conductor plates
separated by some insulation material. The same
amount of charge Q (of opposite polarity) is stored on
the two plates. The voltage V between the two plates is
proportional to the charge Q, but inversely proportional
to the capacitance C of the capacitor:
 We see that capacitance measures the capacity of
capacitor to store charge given a DC voltage, which is
determined by the parameters of the capacitor:
 where A is the overlapping area of the plates and d is
the distance between them.

37. INDUCTOR
 The self-induced voltage, the electromotive force
(emf), across the inductor coil due to a
current i(t) is proportional to the rate of change of
the total magnetic flux ( being the flux in one of
the turns of the coil) caused by the current i(t):


38. STAR AND DELTA CONNECTIONS
 In STAR connection, the starting or finishing
ends (Similar ends) of three coils are connected
together to form the neutral point. A common
wire is taken out from the neutral point which is
called Neutral.
 In DELTA connection, the opposite ends of three
coils are connected together. In other words, the
end of each coil is connected with the start of
another coil, and three wires are taken out from
the coil joints

40. DELTA - STAR TRANSFORMATION

44. STAR - DELTA TRANSFORMATION

45. I N T U I T I V E METHOD OF CIRCUIT
ANALYSIS: SERIES AND
PARALLEL SIMPLIFICATION
 The first move is to collapse a set of resistances
into a single equivalent resistance. Then, found
the current into the equivalent resistance.
Finally, took an expanded view of the two
resistances to determine the specific voltage of
interest.

48. EXAMPLE 1
 Each resistor is of 1Kohm. Calculate equivalent
resistance.
 Ans:5/6 Kohm

49. MESH-CURRENT ANALYSIS(LOOP METHOD)
 Mesh-current analysis is merely an extension of
the use of Kirchhoff’s laws. Figure 31.1 shows a
network whose circulating currents I1, I2 and I3
have been assigned to closed loops in the circuit
rather than to branches. Currents I1, I2 and I3
are called meshcurrents or loop-currents.

50. EXAMPLE 1
Use mesh-current analysis to determine the
current flowing in (a) the 5 ohm resistance, and
(b) the1 ohm resistance of the d.c. circuit.

52. NODE METHOD (NODAL ANALYSIS)
 A node voltage is the potential difference between
the given node and some other node that has
been chosen as a reference node. The reference
node is called the ground.
 Current flows from the node with the higher
potential to the node with the lower potential.

53.  A node of a network is defined as a point where
two or more branches are joined. If three or more
branches join at a node, then that node is called a
principal node or junction. In Figure, points 1, 2,
3, 4 and 5 are nodes, and points 1, 2 and 3 are
principal nodes.

55. EXAMPLE