- Get link
- X
- Other Apps
Electric Network
Topic includes
- Basic Definations
- Kirchhoff's law
- Nodal law
- Superposition theorem
- Thevenin theorem
- Norton's theorem
- Maximum power transfer theorem
Basic Definations
- Circuit
It is a conducting path through which an electric current that flows or is intended to flow.
The various elements of an electric circuit are called parameters, such parameters are resistance, inductance and capacitance.
These parameters may be distributed or not.
- Linear circuit
The circuit whose parameters are constant is known bi linear circuit.
- Non - Linear circuit
The circuit whose parameters change with voltage or current is known as nonlinear circuit.
- Unilateral circuit
Unilateral circuit is one whose properties or characteristics changes with the direction of its operation for example diode, rectifier.
- Bilateral circuit
It is dead circuit whose properties or characteristics are same in either direction.
- Electric Network
An electric network arises when a number of parameters for electric elements coexist or combine in any arrangement.
- Active network
An active network is one which contains one or more than one sources of EMF.
- Passive network
A passive network is one which code not contain any source of EMF.
- Node
A node is junction in a circuit where two or more circuit elements are connected together.
- Branch
The part of a network which lies between two junctions is called or known as branch.
- Potential divider
The potential divider is a high resistance connected across the supply mains and is used to provide a variable voltage from a constant supply voltage.
- Cut set
It means by removing a set of branches from a linear graph without affecting the nodes, two connected subgraphs are obtained and the original graph becomes an connected. The reversal of these branches which results in cutting the graph in two parts is known as the cut set.
- Polarization vector
The polarization vector dielectric polarization is the sum of dipole moments per unit volume is a dielectric material.
- Dielectric strength
- Potential divider
The potential divider is a high resistance connected across the supply mains and is used to provide a variable voltage from a constant supply voltage.
- Cut set
It means by removing a set of branches from a linear graph without affecting the nodes, two connected subgraphs are obtained and the original graph becomes an connected. The reversal of these branches which results in cutting the graph in two parts is known as the cut set.
- Polarization vector
The polarization vector dielectric polarization is the sum of dipole moments per unit volume is a dielectric material.
- Dielectric strength
The maximum field intensity that a dielectric can sustain without breaking down is known as the dielectric strength.
- Polarization density
The induced dipole moment developed per unit volume in a dielectric slab on placing it inside the electric field is known as polarization density.
- Electric dipole
An electric dipole is a combination of two equal point charges of opposite sign separated by a small distance. The small distance is small compared to the distance to the point p at which the electric and potential fields are intended.
- Gauss law
It states that the total displacement for electric flux through any closed surface rounding the charge is equal to the amount of charge enclosed.
The Gaussian surface is used to find the electric field produced by certain sources charges which are otherwise quite difficult to find by the application of Coulomb's law.
- Polarization density
The induced dipole moment developed per unit volume in a dielectric slab on placing it inside the electric field is known as polarization density.
- Electric dipole
An electric dipole is a combination of two equal point charges of opposite sign separated by a small distance. The small distance is small compared to the distance to the point p at which the electric and potential fields are intended.
- Gauss law
It states that the total displacement for electric flux through any closed surface rounding the charge is equal to the amount of charge enclosed.
The Gaussian surface is used to find the electric field produced by certain sources charges which are otherwise quite difficult to find by the application of Coulomb's law.
Kirchhoff's Laws
for complex circuit competitions, the following two laws first stated by Gutsav R. Kirchhoff are indispensable.
First law ( point or current law )
The sum of currents entering a junction is equal to the sum of currents leaving the junction is known as point law.
Second law ( mesh or voltage law )
The sum of EMF around any closed loop of circuit equal to the sum of potential drop in that loop.
•Nodal law
In this method following procedure is adopted.
- Assume the voltage of the different independent nodes.
- write the equations for each mode as per Kirchhoff's current law.
- solve the above equations to get the node voltages.
- calculate the branch current from the value of node voltage.
It may be noted that the above nodal equation contains the following terms:
- the node voltage multiplied why the sum of all conductances connected to that anode. This term is positive.
- dhanyvad voltage at the other end of each branch multiplied by the conductance of branch.
These term is negative.
• Superposition theorem
This theorem is sometimes useful in solution of networks in which some branches may contain sources of EMF.
it is applicable only to Linear networks where current is linearly related to the voltage as per ohm's law.
this theorem states that, in any network containing more than one source of EMF the current in any branch is the algebraic sum of number of individual fictitious currents each of which is due to the separate action of each source of EMF taken to order, when the remaining source of EMF are replaced by conductors, the resistance of which are equal to the internal resistance of respective source.
- the node voltage multiplied why the sum of all conductances connected to that anode. This term is positive.
- dhanyvad voltage at the other end of each branch multiplied by the conductance of branch.
These term is negative.
• Superposition theorem
This theorem is sometimes useful in solution of networks in which some branches may contain sources of EMF.
it is applicable only to Linear networks where current is linearly related to the voltage as per ohm's law.
this theorem states that, in any network containing more than one source of EMF the current in any branch is the algebraic sum of number of individual fictitious currents each of which is due to the separate action of each source of EMF taken to order, when the remaining source of EMF are replaced by conductors, the resistance of which are equal to the internal resistance of respective source.
PROCEDURE
- replace all but one of the source by their internal resistance. If the internal resistance of any source is more as compared to other resistance present in the network, the source is replaced by short circuit.
- find the currents in different branches by using ohm's law.
- repeat the process using each of the EMF as the the sole EMF is time.
The total current in any branch of the current is algebraic sum of current due to its source.
when finding total current in any branch it is necessary to take into account the directions of the current caused by each individual source, current flowing in the same direction being additive, current flowing in opposite direction being subtractive.
• Thevenin theorem
it is quite useful when the current in one branch of a network is to be determined or when the current is an added branch is to be calculated.
it states that for the purpose of determining the current in a resistor, RL connected across two terminals of a network which contains source of EMF and registers, the network can be replaced by single source of EMF and series resistor rth. This EMF eth is equal to potential difference between the terminals of the network when the resistor r is removed, the resistance of series resistor rth is equal to the equivalent resistance of the network with the register r.
EXPLANATION
Let considered the circuit as shown in figure.
- remove RL from the circuit terminals A and B and read draw the circuit shown in figure. Obviously the terminals have been open circuited.
- calculate the open circuit voltage which appears across terminals A and B when they are open. This voltage is ETh.
- short circuit the battery and find the resistance rth of the network as seen from the terminal a and b.
- connect RL back across the terminals A and B from where it was temporarily removed earlier. Current through RL is given by:
• Norton's theorem
As Thevenin theorem was used to simplify a network to a constant voltage source and a series resistance where as Norton's theorem can be used to resolve a network into a constant current source and a parallel resistance.
It states that any two terminal linear network containing independent voltage and current sources may be replaced by an equivalent current IN in parallel with the resistance r and where IN is the short circuit current at network terminals and r n is the equivalent resistance of network as seen from the terminals but with all voltage source is short circuited and all current sources open circuited.
The following procedure may be adopted to determine the Norton's equivalent circuit
- calculate the short circuit current at the network terminals.
- redraw the network with each voltage source replacement short circuit in series with its internal resistance and each current source by an open circuit in parallel with its internal resistance.
- calculate the resistance of the redrawn network as seen from the network terminals.
• Maximum power transfer theorem
This theorem is particularly useful for analysing communication networks.
it states that maximum power output is obtained from a network when the load resistance is equal to the output resistance of the network as seen from the terminals of the load.
Comments
Post a Comment