State the two Kirchhoff’s rules used in electric networks. How are there rules justified?

Asked by Topperlearning User | 8th Jul, 2015, 01:26: PM

Expert Answer:

Kirchhoff’s first rule: 

In any electrical network, the algebraic sum of currents meeting at a junction is always zero.

begin mathsize 12px style sum straight I equals 0 end style

In the junction below, let I1, I2, I3, I4 and I5 be the current in the conductors with directions as shown in the figure below. I5 and I3 are the currents which enter and currents I1, I2 and I4 leave.


According to the Kirchhoff’s law, we have

      (–I1) + (−I2) + I3 + (−I4) + I5 = 0

      Or I1 + I2 + I4 = I3 + I5

Thus, at any junction of several circuit elements, the sum of currents entering the junction must equal the sum of currents leaving it. This is a consequence of charge conservation and the assumption that currents are steady, i.e. no charge piles up at the junction.

Kirchhoff’s second rule: The algebraic sum of changes in potential around any closed loop involving resistors and cells in the loop is zero. 

Answered by  | 8th Jul, 2015, 03:26: PM