Question

The Thevenin resistance of a circuit is zero, then this implies:

• A. The circuit is open-circuited
• B. The circuit behaves as an ideal current source
• C. Maximum power transfer is impossible
• D. The circuit behaves as an ideal voltage source

Hint:

Remember internal resistance characteristics: - Ideal Voltage Source: Internal series resistance \(R_{\text{in}} = 0\). - Ideal Current Source: Internal parallel resistance \(R_{\text{in}} = \infty\).

Answer 1

The Correct Option is D

Concept: The Thevenin equivalent model replaces any active linear network with a single ideal voltage source \(V_{th}\) in series with an internal series resistance \(R_{th}\). The total voltage available at the load terminals under any variable operating load current \(I_L\) is dictated by the linear relationship: \[ V_{\text{load}} = V_{th} - I_L \cdot R_{th} \] An ideal voltage source is characterized by its ability to maintain a completely constant, immutable terminal voltage regardless of the amount of current drawn from or injected into its terminals. This property requires that the internal source impedance be exactly equal to zero, preventing any internal voltage drops.

Step 1: Analyzing the mathematical model for \(R_{th} = 0\).
We are given that the internal Thevenin resistance of the circuit under consideration evaluates to zero: \[ R_{th} = 0\ \Omega \] Substituting this condition into our terminal load voltage expression: \[ V_{\text{load}} = V_{th} - I_L \cdot (0) = V_{th} \] This result demonstrates that the terminal voltage \(V_{\text{load}}\) remains perfectly fixed at \(V_{th}\), completely decoupled from the load current \(I_L\). This behavior defines an ideal voltage source.

Step 2: Evaluating the other options for clarity.

• An open-circuited network implies an infinite internal path resistance, not zero.
• An ideal current source possesses an infinite internal parallel source resistance (\(R_{th} \to \infty\)) so that it delivers constant current regardless of voltage changes.
• Maximum power transfer is still physically possible; if \(R_{th} = 0\), maximum power transfer occurs when the load resistance approaches \(0\ \Omega\), allowing infinite theoretical power transfer from an ideal source.