Thévenin & Norton Equivalent Calculator

Calculate Thévenin voltage, Norton current, and equivalent resistance for any linear circuit.

For power transfer analysis
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Any Linear Two-Terminal Network Can Be Reduced to Two Parameters

Thévenin and Norton equivalents replace a complicated linear network, as seen from two terminals, with a much simpler source-and-resistance model. The Thévenin form is an ideal voltage source VTh in series with RTh. The Norton form is an ideal current source IN in parallel with RN, with RN=RTh and IN=VTh/RTh. They produce the same terminal voltage-current behavior for any attached load.

VTh is the open-circuit terminal voltage. IN is the short-circuit current. For networks containing only independent sources and resistors, RTh can be found by deactivating independent voltage sources to shorts and current sources to opens. Dependent sources must remain active and usually require a test source or Voc/Isc method.

VTh=Voc,   IN=Isc,   RTh=RN=VTh/IN
SymbolMeaningWhy it appears / units
VThThévenin voltageV; open-circuit voltage at the terminals.
INNorton currentA; short-circuit current at the terminals.
RThEquivalent resistanceΩ; resistance seen looking into the linear network.

Once the equivalent is known, changing the load becomes easy. For a resistive load RL, current is VTh/(RTh+RL). Maximum power transfer occurs at RL=RTh for a purely resistive DC equivalent.

Thevenin and Norton forms must predict the same load behavior. They satisfy RN=Rth and IN=Vth/Rth. Connecting the same test load to either equivalent should give the same terminal voltage and current.

Worked Examples

Example 1: V_th=12V, R_th=100Ω, R_L=50Ω
IL=12/(100+50)=0.08A
Result: P_L=0.08²×50=0.32W, P_max=0.36W at RL=100
Not at max power — RL≠Rth
Example 2: V_oc=10V, I_sc=0.05A
R_th=10/0.05=200Ω
Result: Thévenin: 10V, 200Ω — Norton: 50mA, 200Ω
Two equivalent representations
Example 3: Convert Thévenin to Norton
VTh=12V, RTh=4Ω
Result: IN=3A, RN=4Ω
Source transformation preserves the same load behavior.
Example 4: Load current
VTh=12V, RTh=4Ω, RL=8Ω
Result: IL=1A
The original complex network can be replaced by one source and one resistance for this calculation.

Common Mistakes

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Turning off dependent sources

Dependent sources remain active when finding equivalent resistance. Use a test source if necessary.

⚠️
Confusing open-circuit voltage with short-circuit current

VTh is measured with no load current; IN is the current when the output terminals are shorted.

⚠️
Changing equivalent resistance during source transformation

Thévenin and Norton forms use the same resistance value; only the source representation changes.

Frequently Asked Questions

Maximum power transfer theorem?
P_L is maximum when R_L = R_th (load resistance equals source resistance). Then P_max = V_th²/4R_th. Efficiency at max power = 50% (half lost in R_th). Used for antenna matching, audio amplifiers.
Thévenin vs Norton: when to use each?
Thévenin (voltage source + series R): easier when connecting to series loads. Norton (current source + parallel R): easier when connecting to parallel loads. They're equivalent — choose whichever simplifies the analysis.
Why are Thévenin and Norton equivalents useful?
They reduce repeated load calculations to a simple one-source circuit. This is especially useful when the source network stays fixed but the load changes.
Can the theorem be used with AC circuits?
Yes, for linear sinusoidal steady-state circuits, replace resistance by complex impedance and use phasor voltage and current. The same source-transformation ideas apply.
How do I find RTh with dependent sources?
Keep dependent sources active, apply a test voltage or current at the output terminals, and compute RTh=Vtest/Itest. Alternatively use Voc/Isc when both are well defined.
Does the equivalent preserve internal branch currents?
No. It preserves only the terminal voltage-current relationship seen by the load. Internal currents and voltages of the original network are not represented by the reduced equivalent.
How are dependent sources handled when finding Thevenin resistance?
Independent voltage sources are replaced by shorts and independent current sources by opens when appropriate, but dependent sources remain active. With dependent sources present, apply a test voltage or test current at the terminals and compute Rth=Vtest/Itest.

Formula Explorer connections

Interpretation: This formula links charge, voltage, current, resistance, capacitance, power or circuit time response. Assumption: Confirm DC versus AC conditions, RMS versus peak values, component topology and steady-state versus transient behavior. Ideal components may be assumed.

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