Millman's Theorem formula |
||
| \( V \;=\; \dfrac{ \sum \dfrac{ V_i }{ R_i } }{ \sum \dfrac{ 1 }{ R_i } } \) | ||
| Symbol | English | Metric |
| \( V \) = Total Voltage Across the Parallel Circuit | \(V\) | \(V\) |
| \( V_i \) = Voltage Across each Voltage Source | \(V\) | \(V\) |
| \( R_i \) = Resistance Associated with each Voltage Source | \(\Omega\) | \(\Omega\) |
Millman's theorem is an electrical engineering principle used to simplify the analysis of complex circuits with multiple parallel branches, each containing a voltage source and a series impedance. It provides a method to calculate the equivalent voltage across the common nodes of these branches. According to the theorem, the voltage at the common node (or the equivalent voltage across the parallel network) is equal to the sum of the currents contributed by each branch divided by the sum of the conductances (or admittances) of the branches.
This theorem is particularly useful in power systems and circuit analysis, as it reduces the need for solving complex mesh or nodal equations, offering a straightforward way to determine the voltage at a junction point in a network with multiple voltage sources. It assumes linear components and is applicable to both DC and AC circuits, provided impedances are used for AC analysis.
