# Voltage in a Y-Δ transform

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

• Without the voltage sources you didn't need to do anything because there were no voltages and currents. – Curd Jan 1 at 20:06
• 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. – Ben Voigt Jan 1 at 20:10

## 1 Answer

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). simulate this circuit – Schematic created using CircuitLab

Convert each of the Thevenin sources into a Norton source. simulate this circuit

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

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

Done.