Monday, May 27, 2019

KIRCHHOFF'S LAWS (Electrical Networks)

The entire electric circuit analysis is based on Kirchhoff's laws only. But before discussing this, it is essential to familiarise ourselves with the following terms:
(a) Node :-  A node is a junction where two or more circuit elements are connected together.
(b) Branch:-  An element or number of elements connected between two nodes constitutes a branch.
(c) Loop :- A loop is any closed part of the circuit.
(d) Mesh :- A mesh is the most elementary form of a loop and cannot be further divided into other loops. All the meshes are loops but all the loops are not meshes.

(1) Kirchhoff's current law (KCL) :- The algebraic sum of currents meeting at a junction or node in an electric circuit is zero.
Consider five conductors, carrying currents i1,i2,i3,i4 and i5, meeting at a point O as shown in Fig.



Assuming  the incoming current  to be positive and outgoing currents negative, we have

Thus, above law can also be stated as the sum of currents flowing towards any junction in an electric circuit is equal to the sum of the currents flowing away from that junction.

2. Kirchhoff's voltage law (KVL)
The algebraic sum of all the voltages in any closed circuit or mesh or loop is zero.
If we start from any point in a closed circuit and go back to that point, after going round the circuit, there is no increase or decrease in potential at that point. This means that the sum of EMFs and the sum of voltage drops or rises meeting on the way is zero.

Determination of sign   A rise in potential can be assumed to be positive while a fall in potential can be considered negative. The reverse is also possible and both conventions will give the same result.

(a) If we go from the positive terminal of the battery or source to the negative potential and so the emf should be assigned a negative sign. If we go from the negative terminal of or source to the positive terminal, there is a rise in potential and so the emf should be given positive sign.


(b) When current flows through a resistor, there is a voltage drop across it. If we go through the resistance in the same direction as the current, there is a fall in the potential and so the sign of this voltage drop is negative. If we go opposite to the direction of the current flow, there is a rise in potential and hence, this voltage drop should be given a positive sign.


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