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I'm looking for a way to solve the following circuit

Voltage in a delta circuit

Without the voltage sources on the circuit, I would be using a simple Y-Δ transform. But I'm not sure how I should proceed with them on.

Which methods should I use ?

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  • \$\begingroup\$ Without the voltage sources you didn't need to do anything because there were no voltages and currents. \$\endgroup\$ – Curd Jan 1 at 20:06
  • \$\begingroup\$ This circuit isn't large enough that any of the traditional approaches will work, pick between node-voltage, mesh-current, full Kirchoff's and then solve the simultaneous linear equations. Or simplify using Thevenin/Norton equivalence and reduce the resulting parallel sources and resistors. \$\endgroup\$ – Ben Voigt Jan 1 at 20:10
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There is a quite simple way to solve this (without Y-Δ-transform). Here is an outline:

Recognize that nodes A and B are connected by 3 parallel Thevenin sources (= voltage source with resistor in series).

schematic

simulate this circuit – Schematic created using CircuitLab

Convert each of the Thevenin sources into a Norton source.

schematic

simulate this circuit

Those 3 Norton sources can be combined very easily into one Norton source.

schematic

simulate this circuit

If you want, you can transform that combined Norton source back into a Thevenin source.

schematic

simulate this circuit

Done.

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  • \$\begingroup\$ Many thanks. I'll be trying this right away. \$\endgroup\$ – shellwhale Jan 1 at 20:43

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