Enter your branch count and each branch's voltage source and resistance values, and the Millman's Theorem Calculator works out the common node voltage across parallel branches — along with the total conductance and sum of current sources — so you can skip the tedious simultaneous equations.
Common Node Voltage
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Total Conductance
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Sum of Current Sources
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Millman's theorem is used to find the common voltage across parallel branches containing voltage sources and resistances. It's particularly useful when analyzing circuits with multiple voltage sources connected in parallel through resistances.
The theorem converts voltage sources to equivalent current sources, sums all current sources, and divides by the total conductance. The formula is: V = (Σ(Vi/Ri)) / (Σ(1/Ri)), where Vi are the voltage sources and Ri are the resistances.
Millman's theorem only applies to circuits that can be redrawn as parallel branches with voltage sources and resistances. It cannot be used for complex networks with dependent sources or non-linear elements.
Negative voltages are handled normally in the calculation. They represent voltage sources with opposite polarity, and the final result will account for their direction in determining the common node voltage.
Millman's theorem is a simplified version of nodal analysis for circuits with parallel branches. While nodal analysis can handle complex networks, Millman's theorem provides a direct formula for specific parallel circuit configurations.
Yes, Millman's theorem can be applied to AC circuits using complex numbers (phasors) for voltages and impedances instead of resistances. The same mathematical principles apply but with complex arithmetic.
If a resistance approaches zero, that branch becomes dominant and the common voltage approaches the voltage of that branch. In practice, very small resistances can cause numerical instability in calculations.