Kirchoff Law Lecture Notes

In 1847, a German Physicist, Kirchhoff, formulated two fundamental laws of electrici These laws are of tremendous importance from network simplification
point of Kirchhoffs Current Law (KCL).

The law can be stated as, The total current flowing towards a junction point is equal to the total away from that junction point. Another way to state the law is.
The algebraic sum of all the current meeting at a junction point is always zero. The word algebraic means considering the signs of various currents.
Sign convention: Currents flowing towards a junction point are assumed to be positive w currents flowing away from a junction point assumed to be negative.
In fig consider currents I1 and I4 are positive while I2, I3 and I5 arc negative.

Applying KCL

I1- I2 – I3+ I4 – I5 = 0

Kirchhoffs Voltage Law (KVL)

The law can be stated as, “In any network, the algebraic sum of the voltage drops across the circuit elements of any closed path (or loop or mesh) is equal to the algebraic sum of the e.m.f s in the path”

In other words, “the algebraic sum of all the branch voltages, around any closed path or closed loop is always zero.”
Σ (All the emf s in a closed loop ) = 0