What is node analysis?
In electric circuits analysis, nodal analysis, node-voltage analysis, or the branch current method is a method of determining the voltage (potential difference) between "nodes" (points where elements or branches connect) in an electrical circuit in terms of the branch currents.
Supernodes are used to do nodal analysis on circuits containing voltage sources. Supermeshes are used to do mesh analysis on circuits containing current sources. You make a supermesh for each pair of meshes where a current source lies on a branch shared by two meshes.
- Loop: A loop is a closed path in a circuit where two nodes are not traversed twice except the initial point, which is also the final one. But in a loop other paths can be included inside. Mesh: A mesh is a closed path in a circuit with no other paths inside it. In other words, a loop with no other loops inside it.
- 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.
- An 80-mesh screen means there are 80 openings across one linear inch of screen. A 140-mesh screen has 140 openings, and so on. Therefore, as the mesh number increases, the size of the openings decreases.
The voltage drop from a node to the reference node (ground) is called the node voltage. To keep definition simple, node voltages are usually defined with positive polarities. Let's find label node voltages in the following circuit: The circuit has 5 nodes: Two of the nodes have 4 elements connected to them.
- Mesh analysis (or the mesh current method) is a method that is used to solve planar circuits for the currents (and indirectly the voltages) at any place in the electrical circuit. Planar circuits are circuits that can be drawn on a plane surface with no wires crossing each other.
- Supernodes are used to do nodal analysis on circuits containing voltage sources. Supermeshes are used to do mesh analysis on circuits containing current sources. You make a supermesh for each pair of meshes where a current source lies on a branch shared by two meshes.
- At these points the two waves add with opposite phase and cancel each other out. They occur at intervals of half a wavelength (λ/2). Midway between each pair of nodes are locations where the amplitude is maximum. These are called the antinodes.
Supermesh or Supermesh Analysis is a better technique instead of using Mesh analysis to analysis such a complex electric circuit or network, where two meshes have a current source as a common element.
- Kirchhoff's Voltage Law (KVL) is Kirchhoff's second law that deals with the conservation of energy around a closed circuit path. Gustav Kirchhoff's Voltage Law is the second of his fundamental laws we can use for circuit analysis.
- In graph theory, a planar graph is a graph that can be embedded in the plane, i.e., it can be drawn on the plane in such a way that its edges intersect only at their endpoints. In other words, it can be drawn in such a way that no edges cross each other.
- K5: K5 has 5 vertices and 10 edges, and thus by Lemma 2 it is not planar. K3,3: K3,3 has 6 vertices and 9 edges, and so we cannot apply Lemma 2. But notice that it is bipartite, and thus it has no cycles of length 3. In fact, any graph which contains a “topological embedding” of a nonplanar graph is non- planar.
Updated: 26th September 2018