Circuit Theory #28 | Thevenin Resistance with 1 A and 1 V Test Sources

Instructor: Dr. Süleyman Burak ÇELİK

Twenty-eighth lesson in the Circuit Theory series. This lesson continues the same dependent-source Thevenin example and finds `Rth` with two test-source methods. The circuit has a dependent voltage source `2Vx`, a `15 ohm` resistor, a `2 A` current source, a `5 ohm` branch, and a load `R3` at terminals `a-b`. Worked steps: - Start from the known open-circuit result: `Vth = 15 V` - Turn off the independent `2 A` source, so it becomes an open circuit - Keep the dependent source `2Vx` active - Apply a `1 A` test current source and solve `(Vx - 2Vx)/15 + Vx/5 - 1 = 0` - Get `Vx = 7.5 V`, so `Rth = 7.5 ohm` - Apply a `1 V` test voltage source at `a-b` - Use `Vx = 1 V`, `2Vx = 2 V`, and `1/15 + ix = 1/5` - Get `ix = 2/15 A`, so `Rth = 1 / (2/15) = 7.5 ohm` - Build the final Thevenin model: `15 V` in series with `7.5 ohm` Main ideas: - Do not turn off dependent sources by themselves - A killed independent current source becomes an open circuit - A test source measures equivalent resistance at the output terminals - Both test-source methods must agree when signs are tracked consistently