How to Combine Resistors in a Triangular/Diamond Formation?

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SUMMARY

The discussion focuses on finding the Thevenin equivalent of a circuit with resistors arranged in a triangular formation. The solution involves applying a wye-delta transformation to simplify the resistor configuration. The final Thevenin voltage (Vt) is determined to be 10V, and the Thevenin resistance (Rt) is calculated as 30 ohms. Key steps include short-circuiting the voltage source and analyzing the voltage at specific junctions to derive the Thevenin parameters.

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Homework Statement



Find the Thevenin equivalent seen by RL in the figure below:
[PLAIN]http://img708.imageshack.us/img708/7023/thevenineqi.png

Homework Equations


RL = Load resistor

The double-headed arrows indicate that RL is the load

The Attempt at a Solution


I know how to find the Thevenin equivalent in general, but I don't know how to combine the resistors in this problem because they're in a triangular / diamond formation. Can someone help me get started? I don't know which resistors are in parallel and which are in series.

Thanks!

Edit: The answers are Vt = 10V and Rt = 30 ohms
 
Last edited by a moderator:
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This requires a wye-delta transformation.

When you have 3 resistors in a triangular formation with 3 connection points, you need to find a Y-shaped equivalent. That is, one with 3 resistors in a Y-formation such that the resistance from point-to-point remains the same as the original triangular formation.

See:
http://www.play-hookey.com/dc_theory/deriving_delta_y_conversions.html
 
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To find the Thevenin impedance you have to short circuit the voltage source. It seems the load resistor RL is obstructing your imagination. Forget about RL. The short circuit across the voltage source connects the junction of the 30 Ω and 20 Ω resistors to the junction of the 60 Ω and 20 Ω resistors. So you have the parallel combination of the 30 Ω and 60 Ω resistors in series with the parallel combination of the 20 Ω and 20 Ω resistors.
To find the Thevenin voltage also forget about RL with the 60 volt source in place. Find the voltage at the junction of the 30 Ω and 60 Ω resistors (with respect to the negative terminal of the battery. Similarly, find the voltage at the junction of the 20 Ω and 20 Ω resistors. The difference between these voltages is the Thevenin voltage.
Now, can’t you get the Thevenin equivalent of the given cicuit?
 

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