DC NETWORK THEOREMS – PART – 09 – SUBSTITUTION THEOREM

This theorem is based upon substitution of one element by another equivalent element.

Substitution theorem can be used in both linear and nonlinear circuits. This theorem is used to prove several other theorems.

SUBSTITUTION THEOREM

Any branch or network can be replaced by a different branch as long as its potential and current remain unchanged. When the original branch is passive, either a voltage source or a current source is generally used for the substituted branch.

                                                 [OR]

A known voltage to a circuit can be replaced by an ideal voltage source and known current can be replaced by an ideal current source. A resistance R carrying a current I has a voltage drop of IR. Then according to this theorem, this resistor can be replaced by a compensation e.m.f equal to IR. Similarly if the voltage across an element R is V, the element can be replaced by a current source 
I = V/R. No other part of the network is affected by this substitution.

LIMITATIONS

This theorem cannot be applied unless the solution is already known.

APPLICATIONS

This theorem can be applied to any linear, nonlinear, time varying and time invariant.

This theorem is applicable to both time domain and S domain.

This theorem is useful in analyzing the behavior of the network.

DC NETWORK THEOREMS – PART – 08 – COMPENSATION THEOREM

Compensation theorem is useful in finding the changes in current or voltage when the value of resistance is changed in the circuit.

COMPENSATION THEOREM

This theorem states that If the resistance of any branch of a network is changed from R to (R + ΔR) where the current was originally I, then the change of current at any point in the network may be calculated by assuming than an e.m.f. – IΔR has been introduced into the modified branch while all other sources have their e.m.f.s suppressed and are represented by their internal resistance only.

[OR]

This theorem states that any element in the linear, bilateral network, may be replaced by a voltage source of magnitude equal to the current passing through the element multiplied by the value of the element, provided the currents and voltages in other parts of the circuit remain unaltered.

APPLICATIONS

This theorem is useful to calculate the sensitivity of electrical networks and bridges and it is also useful in potentiometer circuits, where a slight change in one resistance results in a shift from a null condition. 

100 PROBLEMS IN ELECTRICAL ENGINEERING - PART – 20 – SIX PROBLEMS ON COMMON GROUND

Many times connection is made to earth which acts as a reference point. The earth or ground has a potential of zero volt with respect to all other points in the circuit.

PROBLEM – 01

Redraw the circuit shown in figure using common ground symbol.

PROBLEM – 02

Redraw the circuit shown in figure using common ground symbol.

PROBLEM – 03

Redraw the circuit shown in figure using common ground symbol.

PROBLEM – 04

Redraw the circuit shown in figure by eliminating the common ground symbol.

PROBLEM – 05

Redraw the circuit shown in figure using common ground symbol.

PROBLEM – 06

Redraw the circuit shown in figure by eliminating the common ground symbol.

PROBLEM – 07

In the circuit find the relative potential of points A,B,C,D,E and F, when A is grounded.

ELECTRICAL ENGINEERING – PART – 23 – EARTHING & GROUNDING

EARTHING means connecting the dead part to the earth.

It means, the part which does not carries current under normal condition to the earth.

Example - electrical equipment’s frames, enclosures, supports etc.

The purpose of earthing is to minimize risk of receiving an electric shock if touching metal parts when a fault is present.

GROUNDING means connecting the live part to the earth.

It means, the part which carries current under normal condition.

Example – grounding of neutral point of a star connected transformer.

The purpose of grounding is the protections of power system equipment and to provide an effective return path from the machine to the power source.

A true earth ground, as defined by the National Electrical Code, physically consists of a conductive pipe or rod driven into the earth to a minimum depth of 8 feet.

The earth was an electrically neutral body, i.e. an equal number of negative and positive charges are distributed throughout the earth at any given time.

Earth is considered to be zero potential and establishes a convenient reference frame for voltage measurement.

Voltmeters read only the difference in potential between two points, absolute measurements can be made by using earth as reference.

The voltage at one point is in a circuit is always measured relative to another point in the circuit, hence, voltage is relative.

The reference point in a circuit is called as ground point. The ground point is used as reference point in the circuit for specifying voltages.

The ground is represented as (i) Earth ground (ii) common ground and (iii) Chassis ground.

CHASSIS – The electronic and electrical components are mounted on a metal base called chassis. Chassis is a good conductor, it provides is conducting return path.

The earth symbol is often used in place of chassis or common ground.

100 PROBLEMS IN ELECTRICAL ENGINEERING - PART – 19 – FIVE PROBLEMS ON SUPERMESH ANALYSIS

SUPERMESH ANALYSIS

It is difficult to apply mesh analysis when any of the branches in the network has a current source.

The two adjacent nodes that are connected by a current source are reduced to single mesh and the equations are formed by applying Kirchhoff's voltage law as usual.

PROBLEM – 01

In the circuit given, find the mesh currents I₁, I₂ and I₃.

PROBLEM – 02

In the circuit given, find the mesh currents I₁, I₂ and I₃.

PROBLEM – 03

In the circuit given, find the mesh currents I₁, I₂ and I₃.

PROBLEM – 04

In the circuit given, find the mesh currents I₁, I₂ and I₃.

PROBLEM – 05

In the circuit given, find the mesh currents I₁, I₂ and I₃.

100 PROBLEMS IN ELECTRICAL ENGINEERING - PART – 18 – SIX PROBLEMS ON SUPERNODE ANALYSIS

SUPERNODE ANALYSIS

It is difficult to apply nodal analysis when any of the branches in the network has a voltage source.

The two adjacent nodes that are connected by a voltage source are reduced to single node and the equations are formed by applying Kirchhoff's current law as usual.

PROBLEM – 01

In the circuit given, find the voltage at node 1, 2 and 3.

PROBLEM – 02

In the circuit given, find the voltage at node 1, 2 and 3.

PROBLEM – 03

In the circuit given, find the voltage at node 1, 2 and 3 and current flow in the 12 ohm resistor.

PROBLEM – 04

In the circuit given, find the voltage at node1, 2 and 3.

PROBLEM – 05

In the circuit given, find the voltage at node 1 and 2.

PROBLEM – 06

In the circuit given, find the voltage at node 1 and 2 and also find the current flow in the 6 ohm resistor.

DC NETWORK THEOREMS – PART – 07 – RECIPROCITY THEOREM

Reciprocity means a relation of mutual dependence, action or influence.

Reciprocity theorem helps to analyze electrical networks and antenna systems.

RECIPROCITY THEOREM

If a source of emf E (or current I) located at one point in a circuit, containing linear bilateral elements, produces a current I (or voltage V) at another point in the circuit, the same voltage E (or current I) acting at the second point will produce the same current I (or voltage V) at the first point.

[OR]

In any linear bilateral network, the current I through any branch of the network due to a single voltage source V elsewhere in the network is equal to the current through the branch of the network where the source was originally placed if the source is placed in the branch in which the current I was originally determined.

LIMITATION

1. This theorem is applicable only to single source network and not to a multi-source network.

2. It is applicable only when the circuit has one independent voltage or current source and not applicable to circuits having dependent sources.

3. The networks should not have any time varying element.

100 PROBLEMS IN ELECTRICAL ENGINEERING - PART – 17 – FIVE PROBLEMS ON NODAL ANALYSIS

PROBLEM – 01

In the circuit given, find the V in the circuit.

PROBLEM – 02

In the circuit given, find the nodal voltages V2 and V3.

PROBLEM – 03

In the circuit given, find the voltages at nodes 1, 2 and 3 and current flow in the 6 ohm resistor.

PROBLEM – 04

In the circuit given, find the nodal voltages V1, V2 and V3.

PROBLEM – 05

In the circuit given, find the values of I1, I2 and I3 and also find the voltage across 6 ohm resistor.