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Norton's theorem states that any linear two-terminal network of sources and resistors can be replaced — as seen from those two terminals — by a single current source IN in parallel with a single resistance RN. It is the current-source counterpart of Thevenin's theorem, and the two are directly related: RN always equals Rth, and IN is the current that would flow if the two terminals were short-circuited.
| Quantity | Formula | Meaning |
|---|---|---|
| Norton current | IN = Vth/Rth | Short-circuit current at the terminals |
| Norton resistance | RN = Rth | Resistance looking in with sources zeroed |
| Back to Thevenin | Vth = IN×RN | Open-circuit voltage |
| Load current | IL = IN×RN/(RN+RL) | Current-divider rule |
Because RN=Rth, converting between the two models is just Ohm's law: divide Vth by Rth to get IN, or multiply IN by RN to get Vth back. This lets you pick whichever model is more convenient — Thevenin (voltage source + series R) for series analysis, Norton (current source + parallel R) for parallel/current-divider analysis.
It states that any linear two-terminal resistive network with sources can be replaced by an equivalent current source IN in parallel with a resistance RN, matching the original network's behavior at those two terminals.
Divide the Thevenin voltage by the Thevenin resistance: IN = Vth/Rth. The resistance stays the same: RN = Rth.
Multiply: Vth = IN×RN. Again the resistance is unchanged.
It is the short-circuit current — the current that flows if you connect a zero-resistance wire directly across the two output terminals.
The resistance seen looking into the two terminals with all independent sources deactivated (voltage sources shorted, current sources opened) — identical to Thevenin resistance.
Norton form is more natural when the load or the rest of the circuit is easier analyzed as resistors in parallel with a current source, e.g. current-divider problems or current-source-driven stages like transistor outputs and solar cells.
IL = IN × RN/(RN+RL) — the Norton current splits between the internal resistance RN and the load RL in inverse proportion to their resistance.
As RL→0 (short circuit), nearly all of IN flows through the load and IL→IN.
As RL→∞ (open circuit), VL→IN×RN, which equals the open-circuit (Thevenin) voltage.
Maximum power is delivered to the load when RL = RN (matched load), at which point half of IN flows through RL. See our Maximum Power Transfer Calculator.
An ideal current source has RN=∞ (infinite parallel resistance), not zero — it always delivers IN regardless of load. RN=0 would short the source and force zero output.
Yes, with impedances instead of resistances: ZN=Zth and IN=Vth/Zth, both generally complex numbers at a given frequency.
Approximately yes for a simplified model: light generates a nearly constant photocurrent (IN) shunted by an internal resistance (RN), which is why the Norton model is common in PV analysis.
A real current source (like a lab supply in current mode) approximates an ideal current source only over a limited compliance voltage range; outside that range it behaves differently, unlike the idealized Norton model.
No — if you already have the Thevenin equivalent (from our Thevenin Equivalent Circuit Calculator), simply convert it using IN=Vth/Rth and RN=Rth as this calculator does.
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