Kirchhoff’s first law (current law or junction rule) : Kirchhoff’s current law states that the algebraic sum of the currents meeting at any junction in a circuit is zero.
The convention is that, the current flowing towards a junction is positive and the current flowing away from the junction is negative. Let 1,2,3,4 and 5 be the conductors meeting at a junction O in an electrical circuit. Let I1, I2, I3, I4 and I5 be the currents passing through the conductors respectively.
According to Kirchhoff’s first law.
I1 + (−I2) + (−I3) + I4 + I5 = 0 or I1 + I4 + I5 = I2 + I3.
The sum of the currents entering the junction is equal to the sum of the currents leaving the junction. This law is a consequence of conservation of charges.
Kirchhoff’s second law (voltage law or loop rule) : Kirchhoff’s voltage law states that the algebraic sum of the products of resistance and current in each part of any closed circuit is equal to the algebraic sum of the emf’s in that closed circuit.
This law is a consequence of conservation of energy. In applying Kirchhoff’s laws to electrical networks, the direction of current flow may be assumed either clockwise or anticlockwise. If the assumed direction of current is not the actual direction, then on solving the problems, the current will be found to have negative sign. If the result is positive, then the assumed direction is the same as actual direction. In the application of Kirchhoff’s second law, we follow that the current in clockwise direction is taken as positive and the current in anticlockwise direction is taken as negative. Let us consider the electric circuit given in Fig.
Considering the closed loop ABCDEFA,
I1R2 + I3R4 + I3r3 + I3R5 +I4R6 + I1r1 + I1R1 = E1 + E3
Both cells E1 and E3 send currents in clockwise direction.
For the closed loop ABEFA
I1R2 + I2R3 + I2r2 + I4R6 + I1r1 + I1R1 = E1 – E2
Negative sign in E2 indicates that it sends current in the anticlockwise direction.
