Thevinin's Theorem

Thevenin's theorem lets you replace any linear two-terminal circuit with a simpler equivalent circuit containing a single voltage source in series with a resistor. This simplification eliminates the need to re-analyze the entire circuit each time the load changes, making it especially useful for circuits with variable loads like household electrical outlets.

The Thevenin voltage is the open-circuit voltage measured across the terminals when no load is connected. With the load removed and the circuit left open, the voltage that appears between the terminals is the Thevenin equivalent voltage. This represents the voltage source component of the Thevenin equivalent circuit.

When the circuit contains no dependent sources, deactivate all independent sources and measure the input resistance seen between the terminals. This resistance value is the Thevenin equivalent resistance. It represents the resistor component of the Thevenin equivalent circuit and determines how the circuit responds to load changes.

When dependent sources exist, deactivate only the independent sources while keeping dependent sources active, since they are controlled by circuit variables. Apply a known test source at the terminals and calculate the resulting terminal voltage or current to determine Thevenin resistance. This approach accounts for the behavior controlled by circuit variables.

Thevenin resistance can be negative in circuits containing dependent sources, indicating that the circuit is supplying power rather than consuming it. This occurs when the dependent sources generate more power than passive elements dissipate, representing an active circuit behavior that differs from typical passive resistance.

A battery can be represented as a Thevenin equivalent circuit where the Thevenin voltage equals the battery's open-circuit voltage and the Thevenin resistance equals its internal resistance. Knowing these parameters allows you to easily calculate current for various loads without re-examining the entire battery circuit.

Once the load is connected to the Thevenin equivalent circuit, use the current divider formula to calculate current through the load. Then apply Ohm's Law to determine the voltage across the load. This two-step approach simplifies analysis compared to examining the original complex circuit.