KIRCHHOFF'S LAW

Kirchhoff's Laws: This law enable us to determine the equivalent resistance of a complex circuit or network and the currents flowing in the various conductors of network.

The following are the two laws of Kirchhoff:

LAW I: Point Law or Current Law

• In any network (or circuit), the algebric sum of the current in all the wires meeting at a point is zero.
• In other words, the sum of the currents flowing towards a point is equal to the sum of the currents flowing away from it.

or       Σ I = 0

For example: Let there be a number of conductors meeting at a junction X as shown in figure

 then we have 

                      i₁ + i₂ + i₃ + i₄ + i₅

             or      i₁ + i₂ + i₃ - i₄ - i₅

             or      incoming currents = outgoing currents

If the incoming currents are taken as positive, then the outgoing currents are taken as negative.

LAW II: Mesh Law or Voltage Law

• In any closed circuit (or mesh), the algebric sum of products of the current and resistance of each part of the circuits is equal to the resultant electromotive force in the circuit.

or        Σ I ∙ R = Σ V

For example: Let the different resistances P, Q, R, S, F and G be connected as shown in figure

Then taking the circuit ABCDA, we have

P i₁ + Q (i₁ + i₂) - S (i₃ -i₁ - i₂) - R (i₃ - i₂) = 0

Again taking the circuit ABDA, we have

P i₁ - G i₂ - R (i₃ -i₁) = V     and so on.