Kirchhoff’s Laws

Kirchhff's Low

 Kirchhoff’s Laws

They were first described in 1845 by German physicist Gustav Kirchhoff. This generalized the work of Georg Ohm and preceded the work of James Clerk Maxwell. Widely used in electrical engineering, they are also called Kirchhoff's rules or simply Kirchhoff's laws. These laws can be applied in time and frequency domains and form the basis for network analysis.
These laws are more comprehensive than Ohm’s law and are used for solving electrical networks which may not be readily solved by the latter. Kirchhoff’s laws, two in number, are particularly useful (a) in determining the equivalent resistance of a complicated network of conductors and (b) for calculating the currents flowing in the various conductors.

The two laws are :
  • Kirchhoff’s Point Law or Current Law (KCL)
  • Kirchhoff’s Mesh Law or Voltage Law (KVL)

Kirchhoff’s Point Law or Current Law (KCL)

It states as follows :
 in any electrical network, the algebraic sum of the currents meeting at a point (or junction) is zero.

Put in another way, it simply means that 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. 

Consider the case of a few conductors meeting at point A as in Circuir-1A. Some conductors have currents leading to point A, whereas some have currents leading away from point A. Assuming the incoming currents to be positive and the outgoing currents negative, 
we have 
             I1 + (−I2) + (−I3) + (+ I4) + (−I5) = 0 
or         I1 + I4 −I2 −I3 −I5 = 0 
or         I1 + I4 = I2 + I3 + I5 
or         incoming currents = outgoing currents

Similarly, in Circuit-1B for node A 

                  + I + (−I1) + (−I2) + (−I3) + (−I4) = 0 
or              I= I1 + I2 + I3 + I4 

We can express the above conclusion thus : 

                          Σ I = 0      a junction

Kirchhoff’s Mesh Law or Voltage Law (KVL)

It states as follows :
 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.Fs. in that path is zero.

 In other words, 
                Σ IR + Σ e.m.f. = 0       ....................................................around a mesh 

It should be noted that algebraic sum is the sum that takes into account the polarities of the voltage drops.

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