Kirchhoff's Laws in Electrical Circuits

Study Notes

Gustav Robert Kirchhoff stated two basic laws in 1847 concerning the relationship between currents and voltages in an electrical network: Kirchhoff’s Current Law (KCL) and the Kirchhoff’s Voltage Law (KVL).

Based on the law of conservation of charge which requires that the algebraic sum of charges within a system cannot change
The algebraic sum of currents entering a node or a closed boundary is zero
KCL mathematically implies that the sum of currents entering (or leaving) a node is zero.
Currents entering a node can be regarded as positive, while currents leaving the node can be taken as negative or vice versa.
The sum of the currents entering a node is equal to the sum of the currents leaving the node.

Based on the law of conservation of energy.
The Algebraic sum of all voltages around a closed path (or loop) is zero
Mathematically, KVL implies that the sum of all voltages in a loop is zero.
KVL can be applied by taking either a clockwise or counterclockwise Trip around the loop.
"Sum of voltage sources = sum of voltage drops"

Allows to replace three resistors in a ∆ configuration by three resistors in a Y configuration and the letter way around.
The transformation of delta (∆) or of a star (Y) into an equivalent delta (∆) may often convert a circuit that is difficult to handle into one that is comparatively simple
These equations are used to transform a delta-connected set of resistances to a wye-connected (Y-connected) set of resistance

The voltage across many types of conducting material is directly proportional to the current flowing through the material, or V = IR
Resistance is normally considered to be a positive quantity although negative resistance may be stimulated with special circuitry.
The simplest passive element, the resistor, was introduced by Georg Simon Ohm, who published a pamphlet in 1827 entitled “Die galvanische Kette mathematish bearbetit” (The Galvanic Circuit Investigated Mathematically).