Thévenin's theorem
A theorem which states that any electric circuit between two terminals containing only resistors, voltage sources, and current sources can be equivalently replaced with a single voltage source and resistor.
Thévenin's theorem: circuit shortcut for analysis
Thévenin's theorem lets you replace a complex network of resistors and sources with a simple equivalent circuit: one voltage source in series with one resistor. This equivalent circuit behaves identically to the original at two specified terminals, no matter what load you connect across them. The theorem applies to linear circuits containing resistors, independent voltage sources, and independent current sources.
The Thévenin equivalent consists of two parts. The Thévenin voltage (V_th) is the open-circuit voltage measured across the terminals when no load is connected. The Thévenin resistance (R_th) is found by zeroing all independent sources (replacing voltage sources with short circuits and current sources with open circuits) and measuring the resistance looking back into the terminals. Once you have V_th and R_th, you can predict current and voltage across any load resistance connected to the original terminals using simple Ohm's law calculations.
When you need it
Circuit analysis becomes tedious when you have a multi-stage network feeding into a load that changes frequently. Rather than solve the entire circuit repeatedly for each load value, find the Thévenin equivalent once. Then for any load, the current through it is simply I = V_th / (R_th + R_load). This saves calculation time in design work, troubleshooting, and impedance matching problems.
The theorem fails for nonlinear elements like diodes and transistors operating outside their linear regions. It also does not apply when you need to find power dissipation inside the source network itself, only at the load terminals. For circuits containing dependent sources (sources controlled by voltages or currents elsewhere in the circuit), the method still works but requires more careful handling when zeroing sources.
Named after the French engineer Léon Charles Thévenin, this theorem is fundamental to circuit theory and remains one of the most practical tools in electrical engineering. Its dual, Norton's theorem, expresses the same equivalence as a current source in parallel with a resistance, and the two are easily converted to each other.