Kirchhoff's laws are particularly useful:
(a) in determining the equivalent resistance of a complicated network of conductors and
(b) for calculating the current flowing in the various conductors.
The two laws are :
Point law or current law (KCL) :-
In any electrical network, the algebraic sum of the currents meeting at a point (or junction ) is zero.
i.e. the total current leaving a junction is equal to the total current entering that junction.
Assuming the incoming current to be positive and the outgoing currents negative, we have
I1 + ( - I2 ) + ( - I3 ) + I4 + (- I5) = 0
Or I1 - I2 - I3 + I4 - I5 = 0
Or I1 + I4 = I2 + I3 + I5
Or Incoming currents = Outgoing Currents
We express the above conclusion thus
∑ Ij = 0 ........................at a junction
Mesh Law or Voltage Law (KVL) :-
The algebraic sum of the products of currents and resistance 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,
∑ I R + ∑ e. m. f. = 0 .............................round a mesh
If one starts from a particular junction and goes round the mesh till one comes back to the starting point, then one must be at the same potential with which one started. Hence, it means that all the sources of e. m. f. meet on the way must necessarily be equal to the voltage drops in the resistance, every voltage being given its proper sign, plus or minus.