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Thevenin & Norton Equivalent Theorems: Two-Terminal Network Simplification

Active two-terminal network → Thevenin or Norton equivalent → connect the same load \(R_L\) and verify identical terminal voltage and current

Circuit Parameters

100 Ω
10 Ω1000 Ω
200 Ω
10 Ω1000 Ω
50 Ω
10 Ω1000 Ω
100 Ω
10 Ω2000 Ω

Equivalent Parameters

Thevenin Voltage \(U_{th}\) — V
Thevenin Resistance \(R_{th}\) — Ω
Norton Current \(I_N\) — A
Norton Resistance \(R_N\) — Ω

Equivalence Verification (Load \(R_L\))

Original \(U_{load}\)
0.00 V
Equivalent \(U_{load}\)
0.00 V
Original \(I_{load}\)
0.00 A
Equivalent \(I_{load}\)
0.00 A
Original Circuit
Thevenin Equivalent
Voltage and current comparison between original and equivalent circuits under the same load

Original Circuit Topology

Original circuit topology

Thevenin Equivalent Circuit

Thevenin equivalent circuit

Theoretical Basis

Any two-terminal network composed of linear elements and independent sources can be replaced, from the perspective of an external load, by a voltage source in series with a resistance (Thevenin) or a current source in parallel with a resistance (Norton).
\(U_{th} = U_s \cdot \frac{R_2}{R_1+R_2}\), \(R_{th} = R_3 + \frac{R_1 R_2}{R_1+R_2}\), \(I_N = U_{th}/R_{th}\).

Equivalence Properties

Regardless of the load \(R_L\) connected, the original circuit and the equivalent circuit have identical V-I characteristics at the a-b terminals.
Thevenin and Norton forms are duals: \(U_{th} = I_N \cdot R_{th}\), \(R_{th} = R_N\).
Adjust the sliders to observe that both sides always match, verifying the equivalence theorem.