page_title: Modified nodal analysis
section_title: Example
hierarchical_section_title: Modified nodal analysis / Example
caption_attribution_description: English: RC Circuit
context_page_description: In electrical engineering, modified nodal analysis or MNA is an extension of nodal analysis which not only determines the circuit's node voltages, but also some branch currents. Modified nodal analysis was developed as a formalism to mitigate the difficulty of representing voltage-defined components in nodal analysis. It is one such formalism. Others, such as sparse tableau formulation, are equally general and related via matrix transformations.
context_section_description: The figure shows a RC series circuit and the table shows the BCE of a linear resistor and a linear capacitor. Note that in the case of the resistor  the admittance  i, , is used instead of . We now proceed as explained above.
  Step 1
  In this case there are two nodes,   and . Also there are three currents: ,  and .
  At node e1 the KCL yields:
  and at node e2:
  Step 2
  With the provided BCEs in the table  and observing that:
  the following equations are the result:
  Step 3
  Note that at this point there are two equations but three unknowns. The missing equation comes from the fact that
  and so finally we have three equations and three unknowns, that leads to a solvable linear system.
caption: Figure 1: RC Circuit.
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