Electric Circuits , Basic definition and Kirchhoff’s Laws KVL, KCL.

Electric Circuits and Network Theorems

   There are certain theorems, which when applied to the solutions of electric networks, wither simplify the network itself or render their analytical solution very easily . These theorems can also be applied to  a.c. system, with the only difference that impedance's replace the ohm resistance of d.c. system. Different electric circuits according to their properties are defined : 

1. Circuit:

 A circuit is a closed conducting path through which an electric current  flows . 

2. Parameters:

 The various elements of an electric circuit are called its parameters like resistance, inductance and capacitance. These parameters may be lumped or distributed. 

3. Liner Circuit:

A linear circuit is one whose parameters are constant  which do not change with voltage or current. 

4. Non-linear Circuit:

 It is that circuit whose parameters change with voltage or current. 

5. Bilateral Circuit:

A bilateral circuit is one whose properties or characteristics are the same in either direction. The usual transmission line is bilateral, because it can be made to perform its function equally well in either direction.

6. Unilateral Circuit:

 It is that circuit whose properties or characteristics change with the direction of its operation. A diode rectifier is a unilateral circuit, because it cannot perform rectification in both directions. 

7. Electric Network:

 A combination of various electric elements, connected in any manner whatever, is called an electric network. 

8. Passive Network:

It is a Network which contains no source of e.m.f. in it. 

9. Active Network:

It is a Network which contains one or more  source of e.m.f. 

10. Node:

  It is a junction in a circuit where two or more circuit elements are connected together.

11. Branch: 

   It is that part of a network which lies between two points . 

12. Loop:

 It is a close path in a circuit in which no element or node is encountered more than once. 

13. Mesh:

  It is a loop that contains number of other loop within it.

Kirchhoff’s Laws  

 Kirchhoff’s laws, two in number, are particularly useful 

(a) in determining the equivalent resistance of a complicated network of conductors 

 (b) for calculating the currents flowing in the various conductors. 

The two-laws are : 

1. Kirchhoff’s Point Law or Current Law (KCL) It states that in any electrical network, the algebraic sum of the currents meeting at a point (or junction) is zero. 

                                                

    or

The total current leaving a junction is equal to the total current entering that junction. It is obviously true because there is no accumulation of charge at the junction of the network.

          

I1 + I2+ I3 + (- I4) + (-I5) = 0  or   I1 + I2+I3 = I4+ I5 

2. Kirchhoff’s Mesh Law or Voltage Law (KVL): 

It states that the algebraic sum of the products of currents and resistances in each of the conductors in any closed path (or mesh) in a network plus the algebraic sum of the e.m.f's. in that path is zero. In other words, Σ IR + Σ e.m.f. = 0 ...round a mesh It should be noted that algebraic sum is the sum which takes into account the polarities of the voltage drops

         

V1+V2=IR1+IR2   or   V1+V2-IR1-IR2=0