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Thevenin's Theorem

 

Thevenin's Theorem formulas

\(  V_{th} \;=\;  V_{oc} \)     (Voltage)

\(  R_{th} \;=\;  R_{eq} \)     (Resistance)

\(  I_{L} \;=\;  \dfrac{ V_{th}  }{  R_{th} + R_{L} }   \)     (Current)
Symbol English Metric
\( V_{th} \) = Thevenin's Theorem Voltage \(V\) \(V\) 
\( V_{oc} \) = Open-circuit Voltage Across the Terminal \(V\) \(V\)
\( R_{th} \) = Thevenin's Theorem Resistance \(\Omega\) \(\Omega\)
\( R_{eq} \) = Equivalent Resistance Across the Terminal \(\Omega\) \(\Omega\)
\( I_{L} \) = Thevenin's Theorem Current \(A\) \(A\)
\( R_{L} \) = Load Resistor Connected Across the Terminal \(\Omega\)  \(\Omega\) 

Thevenin's theorem is a principle in electrical engineering that simplifies the analysis of complex linear electrical circuits.  It states that any linear circuit containing multiple voltage and current sources, as well as resistances, can be replaced by an equivalent circuit consisting of a single voltage source, known as the Thevenin equivalent voltage (\(V_{th}\)), in series with a single resistance, called the Thevenin equivalent resistance (\(R_{th}\)).  This equivalent circuit is valid with respect to a specific pair of terminals in the original circuit. 

The theorem is useful for analyzing circuits with a variable load, as it allows engineers to simplify the circuit to a single voltage source and resistor, making it easier to calculate the current, voltage, or power delivered to the load.   Thevenin's theorem is widely applied in circuit design, power systems, and electronics to streamline analysis and improve efficiency.

The Thevenin's theorem itself does not have a single, standalone formula.  Instead, it's a method for finding two key values that define an equivalent circuit, Thevenin voltage (\(V_{th}\)) and Thevenin resistance (\(R_{th}\)).  Once these values are found, the complex circuit can be replaced by a simple series circuit.
Thevenin Equivalent Voltage (\(V_{th}\))  -  This is the open-circuit voltage across the terminals of interest.  It is calculated by finding the voltage difference between the two terminals when no load is connected.
Thevenin Equivalent Resistance (\(R_{th}\))  -  This is the equivalent resistance seen across the terminals when all independent sources are deactivated (voltage sources replaced by short circuits, current sources replaced by open circuits).
Thevenin Equivalent Current (\(I_{L}\))  -  Once \(V_{th}\;\) and \(R_{th}\;\) are determined, the Thevenin equivalent circuit is a voltage source \(V_{th}\;\)in series with a resistor \(R_{th}\).  For a load resistor \(R_{L}\;\)connected across the terminals, the current through the load can be found using Ohm's Law.

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