The superposition theorem for electrical circuit states that for a linear system the response (voltage or current)
in any branch of a bilateral linear circuit having more than one
independent source equals the algebraic sum of the responses caused by
each independent source acting alone, where all the other independent
sources are replaced by their internal impedances.
To ascertain the contribution of each individual source, all of the other sources first must be "turned off" (set to zero) by:
Replacing all other independent voltage sources with a short circuit (thereby eliminating difference of potential i.e. V=0; internal impedance of ideal voltage source is zero (short circuit)).
Replacing all other independent current sources with an open circuit (thereby eliminating current i.e. I=0; internal impedance of ideal current source is infinite (open circuit)).
Example:
Find R2;
The figure has two(2) voltage source, in order to get the voltage across R2, we need to get first the voltage that being supplied on the other loop by deactivating/turning off the other source.
As you can see, the B2 is already turned off, therefore we can solve it using the voltage division principle. -The Voltage division can be seen on the past blog for more information!
After that, the B1 must be turned off and B2 is now on in order to get the voltage on the other loop.
I'm sure, we can get now the total voltage that R2 have.
TAKE NOTE: When there is Three(3) or more sources in a circuit, only 1 must be turned on and the rest is disable.
A Mesh is a loop that does not contain any other loop within it.
~ a loop can be a mesh, but a mesh can't be a loop.
Same as the nodal analysis, a mesh analysis have also a steps in getting the equation but they differ for some aspects which is the Nodal analysis talks about the nodal voltages while the Mesh analysis talks about mesh currents.
~ a mesh current 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.
Why is it QUITE SIMILAR TO THE BRANCH CURRENT?
- it is quite similar, then of course it is also quite different but it depends on how the mesh is being ISOLATED.
There are steps in determining mesh currents same as nodal analysis, there are steps to determine nodal voltage in order to form an equation.
STEPS TO DETERMINE MESH CURRENTS:
1. Assign mesh currents I1, I2,... In to the n meshes.
2. Apply KVL to each of the n meshes. Use ohm's law to express the voltages in terms of the mesh currents.
3. Solve the resulting n simultaneous equations to get the mesh currents.
Example:
As you observe the figure, the current flow counter clockwise but wherever the mesh currents will flow, it's direction is arbitrary and does not affect the validity of the solution.
~ as a class, we are more prefer to have the mesh currents direction clockwise because for us it is more convenient and easier to analyze.
Mesh analysis with current sources
Case 1:
When a current source exists only in one mesh
Case 2:
When a current source exists between two meshes and that is SUPERMESH.
What is supermesh?
A SUPERMESH results when two meshes have current source in common.
As we go through the "Nodal Analysis" topic which includes the KCL and KVL and the SUPERNODE, we come up with a lot of problem solving then we have two method in solving/analyzing the circuit, which is the short cut method and the long way method. The short cut method,
The nodal voltage must be determined.
it gives the adjacent of the resistors into voltage.
The long way method,
The nodal voltages must be determined.
The flow current of the current must be assigned.
#REMINDERS ~ The current leaving is positive, and the current entering is negative.
WYE - DELTA TRANSFORMATION
The wye - delta transform, also written wye-delta and also known by many other
names, is a mathematical technique to simplify the analysis of an
electrical network.
wye - Y
delta - Δ
~ I think why the wye-delta transformation are made because usually in a circuit(complicated design) have a form of Y and Δ in order to get the total resistance.
