Explain Node-voltage and mesh-current analyses?

The node-voltage and mesh-current methods, which complement each other, are well-ordered systematic methods of analysis for solving complicated network problems. The former is based on the KCL equations, whereas the KVL equations form the basis for the latter. In both methods an appropriate number of simultaneous algebraic equations are developed. The unknown nodal voltages are found in the nodal method, whereas the unknown mesh currents are calculated in the loop (or mesh) method. A decision to use one or the other method of analysis is usually based on the number of equations needed for each method.

Even though, for simplicity, only resistive networks with dc voltages are considered in this section, the methods themselves are applicable to more general cases with time-varying sources, inductors, capacitors, and other circuit elements.