1 Answer
Millman’s Theorem is a method used to simplify complex electrical circuits that have multiple branches in parallel with different voltage sources and resistances. The theorem gives us a way to find the voltage at the common node in such circuits without having to solve the entire circuit step by step.
The Conclusion of Millman’s Theorem:
The voltage at the common node (also called the resultant voltage) in a network of parallel branches with multiple voltage sources and resistances is given by:
\[
V_{\text{resultant}} = \frac{\sum \left( \frac{V_i}{R_i} \right)}{\sum \left( \frac{1}{R_i} \right)}
\]
Where:
Summary:
The conclusion is that by using Millman’s Theorem, you can easily find the voltage at the node by summing up the contributions of each voltage source, weighted by their conductance (which is the reciprocal of resistance), and then dividing that sum by the total conductance.
This approach simplifies solving circuits with multiple parallel voltage sources, especially when you don't want to go through solving mesh or nodal analysis manually.
The Conclusion of Millman’s Theorem:
The voltage at the common node (also called the resultant voltage) in a network of parallel branches with multiple voltage sources and resistances is given by:\[
V_{\text{resultant}} = \frac{\sum \left( \frac{V_i}{R_i} \right)}{\sum \left( \frac{1}{R_i} \right)}
\]
Where:
- \(V_i\) = Voltage of the i-th source
- \(R_i\) = Resistance in the branch with the i-th voltage source
Summary:
The conclusion is that by using Millman’s Theorem, you can easily find the voltage at the node by summing up the contributions of each voltage source, weighted by their conductance (which is the reciprocal of resistance), and then dividing that sum by the total conductance.This approach simplifies solving circuits with multiple parallel voltage sources, especially when you don't want to go through solving mesh or nodal analysis manually.