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Thévenin and Norton Equivalent Calculator

Any linear network, however complicated, looks from two terminals like a single voltage source behind a single resistance. That is Thévenin's theorem, and it turns a repeated load calculation into a one-line answer.

Thévenin / Norton & Max Power Transfer

From a Thévenin equivalent (V_th, R_th) get the Norton current and the maximum power a load can draw. Add a load resistance R_L to see the actual current, voltage and power delivered.

Norton current I_N
Max power to load P_max
  1. 1.Given Thévenin source: V_th = 12 V, R_th = 4 Ω
  2. 2.FormulaNorton current I_N = V_th ÷ R_th (= short-circuit current)SubstituteI_N = 12 ÷ 4ResultI_N = 3 A
  3. 3.FormulaMax power to a load P_max = V_th² ÷ (4·R_th)SubstituteP_max = 12² ÷ (4 × 4)ResultP_max = 9 W (at R_L = R_th)
Common trap: Maximum power transfer (R_L = R_th) is not maximum efficiency — at the match, half the power is burnt inside R_th, so efficiency is only 50%. Power systems deliberately run with R_L ≫ R_th for high efficiency; impedance matching is for signals, not power delivery.

The formula

V_th = open-circuit voltage ; R_th = resistance with sources removed ; I_N = V_th / R_th

V_th
Thévenin voltage — the open-circuit terminal voltage (volts)
R_th
Thévenin resistance seen from the terminals, sources zeroed (ohms)
I_N
Norton current — the short-circuit terminal current (amperes)

Worked example

A 12 V source with R₁ = 6 kΩ in series, and R₂ = 3 kΩ across the output terminals.

  1. Open-circuit voltage is a divider: V_th = 12 × 3 / (6 + 3) = 4 V
  2. Short the source and look back: R_th = 6 kΩ ∥ 3 kΩ = 2 kΩ
  3. Norton form: I_N = 4 / 2000 = 2 mA in parallel with 2 kΩ

V_th = 4 V with R_th = 2 kΩ, equivalently a 2 mA source in parallel with 2 kΩ.

Where you'll use it

Maximum power transfer problems, working out what a load will actually receive, and any question that asks for the current through one branch while everything else stays fixed. Maximum power reaches the load when R_load = R_th — at 50 % efficiency, which is why power systems never run there.

The laws behind it

Parts this applies to

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