In a circuit with a dependent source, how would you determine the Thevenin resistance seen by the load?

In a circuit with a dependent source, how would you determine the Thevenin resistance seen by the load?

• A. Apply a test source with dependent sources active to determine R_th
• B. Deactivate all sources and measure resistance
• C. Replace dependent source with a fixed value
• D. Short the load and measure current

Answer: (A)

When a circuit includes dependent sources, the Thevenin resistance seen from the load cannot be found by simply deactivating all sources. The dependent source’s behavior depends on circuit variables, so you must probe the port with a test excitation while keeping the dependent source active. Apply a known test source at the load terminals (either a voltage source or a current source). If you apply a test voltage Vt and measure the resulting current It into the port, then the Thevenin resistance is Rth = Vt / It. If you use a test current source and measure the resulting voltage, Rth = Vt / It still holds. This approach captures how the dependent source affects the port response. The other options miss this crucial point: deactivating independent sources alone can’t reveal the correct interaction with the dependent source, replacing the dependent source with a fixed value ignores its controlling behavior, and simply shorting the load doesn’t provide the necessary voltage-current relationship to determine Rth.

When a circuit includes dependent sources, the Thevenin resistance seen from the load cannot be found by simply deactivating all sources. The dependent source’s behavior depends on circuit variables, so you must probe the port with a test excitation while keeping the dependent source active. Apply a known test source at the load terminals (either a voltage source or a current source). If you apply a test voltage Vt and measure the resulting current It into the port, then the Thevenin resistance is Rth = Vt / It. If you use a test current source and measure the resulting voltage, Rth = Vt / It still holds. This approach captures how the dependent source affects the port response. The other options miss this crucial point: deactivating independent sources alone can’t reveal the correct interaction with the dependent source, replacing the dependent source with a fixed value ignores its controlling behavior, and simply shorting the load doesn’t provide the necessary voltage-current relationship to determine Rth.