Super Mesh Analysis Solved Problems

This is an equation that relates the dependent source’s variable to the voltage or current that the source depends on in the circuit.

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A dependent source is a current source or voltage source that depends on the voltage or current of another element in the circuit.

When a dependent source is contained within an essential mesh, the dependent source should be treated like an independent source.

In supermesh circuit analysis technique, the current source is in the inner area of the supermesh.

Therefore, we are able to reduce the number of meshes by one (1) for each current source which is present in the circuit.

A more general technique, called loop analysis (with the corresponding network variables called loop currents) can be applied to any circuit, planar or not.

Mesh analysis and loop analysis both make use of Kirchhoff’s voltage law to arrive at a set of equations guaranteed to be solvable if the circuit has a solution.This will be an equation where the current source is equal to one of the mesh currents minus the other.The following is a simple example of dealing with a supermesh.This helps prevent errors when writing out the equations.The convention is to have all the mesh currents looping in a clockwise direction.Figure 1 labels the essential meshes with one, two, and three.A mesh current is a current that loops around the essential mesh and the equations are set solved in terms of them.This is because there are fewer mesh currents than there are physical branch currents.In figure 2 for example, there are six branch currents but only three mesh currents. These equations are the sum of the voltage drops in a complete loop of the mesh current.If a voltage source is present within the mesh loop, the voltage at the source is either added or subtracted depending on if it is a voltage drop or a voltage rise in the direction of the mesh current.For a current source that is not contained between two meshes, the mesh current will take the positive or negative value of the current source depending on if the mesh current is in the same or opposite direction of the current source.