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Thevenin Resistance from an Open-Circuit and Loaded Measurement

Also known as Thevenin equivalent resistance · internal resistance · source resistance · output impedance from load test · Thevenin voltage

RTh=RL(VOCVL−1)R_{Th} = R_{L} \left( \frac{V_{OC}}{V_{L}} - 1 \right)

Worked example: 9.00 V open, 8.10 V into 100 Ω → 11.11 Ω internal — press Try an example to run it live, then adjust anything.

Enter your known values, leave one input blank, and solves for the missing one. Tap a variable’s symbol to see what it means, with a typical value. Try different units for next level excitement!

See also
Norton Current from the Thevenin Equivalent — Turns the same equivalent into its current-source twin.Maximum Power Transfer to a Matched Load — Once R_Th is known, this is the load that extracts the most power from the source.
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Thevenin from two readings →

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Thevenin Resistance from an Open-Circuit and Loaded Measurement explained

RThVOCRLVL

Léon Thévenin's 1883 theorem says something extravagant: any tangle of sources and resistors, seen from two terminals, behaves exactly like one voltage source behind one resistor. You never have to know what is inside. And you can measure both numbers with a voltmeter and one known resistor — read the open-circuit voltage, hang the load, read the sagged voltage, and the internal resistance falls out of the droop.

Work an example the long way and the formula becomes obvious. A 9 V cell reads 9.00 V open and 8.10 V across 100 Ω. That load is drawing 8.10/100=0.0818.10/100 = 0.081 A, and the 0.90 V that went missing was dropped inside the cell, so RTh=0.90/0.081=11.1R_{Th} = 0.90/0.081 = 11.1 Ω. A fresh alkaline should be well under 2 Ω, so this one is tired — which is exactly how a battery tester works.

The mistake to avoid is shorting the terminals to find the internal resistance directly. On a cell that is merely rude; on a car battery or a lithium pack it is a welding accident. Use a load that draws a sensible current and let the droop tell you. One caution on the theorem itself: it holds for linear circuits only. Put a diode, a lamp filament or a switching supply behind the terminals and RTh becomes a number that changes with the load you used to measure it.

Thevenin Resistance from an Open-Circuit and Loaded Measurement formula

RTh=RL(VOCVL−1)R_{Th} = R_{L} \left( \frac{V_{OC}}{V_{L}} - 1 \right)
Where
  • RThR_{Th}= Thevenin resistance (Ω)
  • VOCV_{OC}= Open-circuit voltage (V)
  • VLV_{L}= Loaded terminal voltage (V)
  • RLR_{L}= Load resistance (Ω)

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