NODE AND MESH

• NODE VOLTAGE METHOD

In the node voltage method, one of the principle nodes is selected as the reference and equations base on Kirchoff Current Law (KCL) are written at the other principles nodes.

FIGURE 1

The network shown in figure 1 contains five nodes, where 11 and 22 are simple node and 1, 2, and E₀ are principal node.
Node E0 selected as the reference for voltage V1 and V2. KCL requires that the total out of node 1 be zero.

Total current out of node 2 must be zero.

• MESH CURRENT METHOD

The Mesh Current Method, also known as the Loop Current Method, is quite similar to the Branch Current method in that it uses simultaneous equations, Kirchhoff's Voltage Law, and Ohm's Law to determine unknown currents in a network. Steps to follow for the “Mesh Current” method of analysis: 

1. Draws mesh currents in loops of circuit, enough to account for all components.
2.  Label resistor voltage drop polarities based on assumed directions of mesh currents.
3. Write KVL equations for each loop of the circuit, substituting the product IR for E in each resistor term of the equation. Where two mesh currents intersect through a component, express the current as the algebraic sum of those two mesh currents (i.e. I₁ + I₂) if the currents go in the same direction through that component. If not, express the current as the difference (i.e. I₁ - I₂).
4. Solve for unknown mesh currents (simultaneous equations).
5.  If any solution is negative, then the assumed current direction is wrong.
6. Algebraically add mesh currents to find current in components sharing multiple mesh currents.
7.  Solve for voltage drops across all resistors (E=IR).