Kirchoff's Current Law (KCL)

"The algebraic sum of all currents coming or leaving a node in an electric circuit isequal to zero." In other words, the sum of currents entering is equal to the sum of currents leaving the node in an  electric circuit. Consider node B in Figure, then according to KCL

 

Example

For circuit diagrams shown in Figure below, write down the nodal equations

Circuit diagrams to demonstrate application of KCL in above example. Figure (a) contains 1 node excluding the reference, thus 1 equation is required.

 

If I_s, R₁, R₂ and R₃ are know in Equation given above, V can be determined. In Figure b), 2 equations are written for the 2 nodes labelled V₁ and V₂.

Equations can be simultaneously solved to determine the node voltages provided resistors' values and I_s are known.

Figure (c) contains 3 nodes hence 3 equations are required to solve for node voltages V₁, V₂ and V₃.

Node voltages V₁, V₂ and V₃ can be calculated by simultaneously solving Equations obtained above and by using Cramer's rule.

Resistors in Parallel

Consider Figure given below with a single current source and 2 resistors connected in parallel. All the parallel circuit elements have same voltage, V across them that is V₁ = V₂ =V

 

By applying KCL at node A

I_s =I₁ +I₂

 

here R_eq is equivalent resistance of parallel, 2 network of resistors. For the n number of resistors connected in parallel, combined resistance can be given by
 

or in the terms of conductance, G

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