ELECTRIC CIRCUIT

ELECTRIC CIRCUIT

➢ STATES OF ELECTRIC CIRCUIT 

• There are three states 

1. Open circuit

• In circuit, the switch is open.

• An open circuit is one where the continuity has been broken by an interruption in the path for current to flow.

2. Closed circuit

• In circuit, a switch is closed.
• open circuit is a circuit which has no complete path to pass the current through.

3. Short circuit

• A short circuit is simply a low resistance connection between the two conductors supplying electrical power to any circuit.

• A short circuit is where the voltage tends to zero and current tends to infinity.

➢ SERIES CONNECTION OF RESISTORS

• When the resistors are connected end to end, so that they from only one path for the flow of current, then resistors are said to be connected in series and such circuits are known as series circuits.

V = V1+ V2+ V3

I R = I R1 + I R2 +I R3

I R= I ( R1 + R2 + R3)

R = R1 + R2 + R3

➢ PARALLEL CONNECTION OF RESISTORS

• When a number of resistors are connected in such a way that one end of each of them is joined to a common point and the other ends being joined to another common point then resistors are said to be connected in parallel and such circuit 

are known as parallel circuits.

I= I1+ I2+ I3

(𝑉/𝑅)=(𝑉/R1)+(𝑉/R2)+(𝑉/R3)

(1/𝑅)=(1/R1)+(1/R2)+(1/R3)

➢ TOPOLOGY OF CIRCUIT

1. Active element

This is source of emf or current. Source of emf gives constant electromotive force 

where as the current source supplies constant current. In fig is the voltage source while is the current source.

2. Passive element :

In d.c.circuit passive element is the resistance only.

3. Network :

Circuit made by the connection of active element or passive element or active and passive both element is called network.

4. Node :

The point at which two or more element meet is called the node.

5. Branch :

Element or group of element connected between two nodes is called branch.

6. Loop : 

Any closed path in a network is called loop.

7. Mesh :

Mesh is a single open loop that does not have a closed path. There are no components inside a mesh.

➢ KIRCHOFF’S LAW

• There are two laws

1) Kirchhoff’s current law (KCL) or point:

According to this law in any network or wires carrying currents the algrabicsum of all current meeting at a point is zero.

Or 

The sum of incoming current towards any outgoing current away from 

that point.

 • If I1, I2, I3, I4,I5 and I6 are the currents meeting at junction taking incoming current positive and outgoing current as negative.

I1 − I2 − I3 + I4 + I5 − I6= 0

or

I1+ I4 + I5 = I2 + I3 + I6

2) Kirchhoff’s voltage law (KVL) OR mesh law:

According to this law in any closed circuit or mesh the algebraic sum of voltage in a loop is zero. 

Or

Sum of voltage drops equal to the sum of voltage rise.

−E1 − I1R1 + E2 + I2R2= 0

Or

E2+I2R2= E1+I1R1

➢ MAXWELL LOOP CURRENT METHOD

• It a network with several sources has more than two nodes the current in it may be determined by this theorem. This is one of the most universal methods for solving networks.

• This theorem involves representing a current that is assumed to circulate around a closed loop by a curved arrow and labelling the arrow with its identifying current flowing through the branch common to two meshes will be equal to the algebraic sum of the two loop current flowing through it.

• The direction of any loop current may be taken either as clockwise or counter-clockwise but for systematic solution the directions of all loop currents are assumed to be the same .

• Then Kirchhoff's second law is applied to each mesh and algebraic equations are obtained. 

• The total number of independent equation are obtained.

• The total number of independent equation is equal to the number of meshes.

• Therefore, they can be solved as simultaneous equation to give the circulating currents and then the branch current.

• Thus, this method eliminates a great deal of tedious calculation work involved in the branch current method.

➢ MESH ANALYSIS

• Kirchhoff’s voltage law leads to the mesh or loop analysis of a circuit. 

• Kirchhoff’s voltage law state that the algebraic sum of all the voltage in a closed loop is zero.

• In this method current re assumed in different branches.

• Number of equations required are equal to the number of unknown currents.

➢ NODAL ANALYSIS

• A network can also be analysed using nodal analysis.

• This analysis is found useful when voltage at different nodes are required to be found.

• Assume one reference node and using Kirchhoff's current law find the different branch current.

• In this admittance are written in place of Z.

➢ PRINCIPAL OF DUALITY

• Two physical system, or phenomenon are called dual.

• Principal of duality only implies that circuit equations are of the same mathematical from and dual network behave similarly but with interchanged variables.

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