Electrical Engineering Circuit Laws

**Circuit laws**

Two important laws are based on the physical properties of electric charges and these laws form the foundation of circuit analysis. They are Kirchhoff’s current law and Kirchhoff’s voltage law. While Kirchhoff’s Current Law (KCL) is based on the principle of conservation of electric charge, Kirchhoff’s Voltage Law (KVL) is based on the principle of energy conservation.

**Kirchhoff’s Current Law**

At any instant, the algebraic sum of the currents i entering a node in a circuit is equal to zero. The application of KCL at node C yields the following equation:

i_{1}+ i_{2}+ i_{3 }= 0

similarly at node D, KCL yields:

i_{1 }- i_{2}- i_{3 }= 0

**Kirchhoff’s Voltage Law**

At any instant, the algebraic sum of the voltages (v) around a loop is equal to zero. In going around a loop, a useful convention is to take the voltage drop (going from positive to negative) as positive and the voltage rise (going from negative to positive) as negative.

**Circuit Analysis**

Analysis of an electrical circuit involves the determination of voltages and currents in various elements, given the element values and their interconnections. In a linear circuit, the v-i relations of the circuit elements and the equations generated by the application of KCL at the nodes and of KVL for the loops generate a sufficient number of simultaneous linear equations that can be solved for unknown voltages and currents. Various steps involved in the analysis of linear circuits are as follows.

For all the elements except the current sources, assign a current variable with arbitrary polarity. For the current sources, current values and polarities are given.

For all the elements except the voltage sources, assign a voltage variable with polarities based on the passive sign convention. For voltage sources, the voltages and their polarities are known.

Write KCL equations at N-1 nodes, where N is the total number of nodes in the circuit.

Write expressions for voltage variables of passive elements using their v-i relations.

Apply KVL equations for E-N+1 independent loops, where E is the number of elements in the circuit. In the case of planar circuits, which can be drawn on a plane paper without edges crossing over one another, the meshes will form a set of independent loops. For non-planar circuits, use special methods that employ topological techniques to find independent loops.

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