Does a Thevenin Equivalent Circuit Accurately Predict Power in Variable Loads?

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In a thevenin equivalent circuit are you able to find the power used in the circuit by the variable load?
I have a circuit where the variable load is in parrallel I was thinking the power used in the original circuit by the variable load would be different than in the equivalent because it is in series.. Any ideas?
 
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It's called the Thevinin Equivalent because its equivalent and it's purpose is to do exactly what you mention with it, that is convert a messy / complicated / busy circuit to a simple one so you can figure out some end result.

Why not try both ways and see for yourself!