Electrical – Thevenin equivalent with independent source

circuit analysisthevenin

I'm struggling with analyzing this circuit:

schematic

simulate this circuit – Schematic created using CircuitLab

\$R_1 = 5\Omega\$

\$R_2 = 5\Omega\$

\$R_3 = 2.5\Omega\$

\$R_4 = 5\Omega\$

Voltage source = 5 V

The task is to determine the Thevenin equivalent (Vth and Rth) between a and b respectively (black boxes). I'm not sure how to approach this question. Could anyone help me to get started?

Best Answer

The best way to solve these examples is usually by using source transformations.

  1. Convert V1 into a current source V1/R2 --> I1 = 5V/5ohm = 1A. R2 is now parallel to the current source.
  2. Combine R1 and R2 (they are now parallel) -> R = 2.5 ohm
  3. Convert the current source back to a voltage source, V = I1 * R = 2.5V. R is now in series with the voltage source.
  4. Combine R with R3 --> R' = 5 ohm
  5. Convert this back to a current source I = 2.5V / 5ohm = 0.5A. R' is now parallel to the current source and parallel to R4.
  6. Combine R' and R4: Rth = 2.5ohm
  7. Convert the current source back to voltage source Vth=0.5A*Rth = 1.25V

This seems difficult, but with a little practice this is the quickest way.

The result is Vth=1.25V and Rth=2.5, which agrees with the result from the simulation.

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