Calculation
Ri = (U1 − U2) / (I2 − I1)
Between any two load points of the same source, terminal voltage changes linearly with current; the slope of that line is the internal resistance.
Busch 2006, Abschnitt 4.1.4 Der Grundstromkreis, Gl. (4.9)/(4.10)
Source internal resistance from two load points
Between any two load points of the same source, terminal voltage changes linearly with current; the slope of that line is the internal resistance.
MINTSI
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Result
Select a target and calculate.
Understand the inputs
- Internal resistance Ri — Source internal resistance found from the slope of the terminal-voltage characteristic.
- Terminal voltage at first point U1 — Measured terminal voltage at the lighter load (smaller current I1).
- Load current at first point I1 — Measured current at the first point; must be smaller than I2.
- Terminal voltage at second point U2 — Measured terminal voltage at the heavier load (larger current I2).
- Load current at second point I2 — Measured current at the second point; must exceed I1.
Example
U1=12 V at I1=1 A and U2=11 V at I2=6 A give Ri=(12−11)/(6−1)=0.2 Ω.
Assumptions and limits
Linear source with Ri constant over the measurement range; state-of-charge change during measurement, temperature drift and dynamic behaviour are excluded.
Understand Source internal resistance from two load points
This calculator determines a real voltage source's internal resistance from just two measured operating points, with no need to know open-circuit voltage. It complements the existing terminal-voltage calculator, which already assumes Uq.
What does this quantity describe?
Since Uterm=Uq−Ia·Ri describes a straight line in the U-I plane, Ri follows directly as the slope between two measured points: Ri=(U1−U2)/(I2−I1).
Formula and variables
Ri = (U1 − U2) / (I2 − I1)
Ri = (U1 − U2) / (I2 − I1)
| Symbol / input | Meaning |
|---|---|
| Internal resistance Ri | Source internal resistance found from the slope of the terminal-voltage characteristic. |
| Terminal voltage at first point U1 | Measured terminal voltage at the lighter load (smaller current I1). |
| Load current at first point I1 | Measured current at the first point; must be smaller than I2. |
| Terminal voltage at second point U2 | Measured terminal voltage at the heavier load (larger current I2). |
| Load current at second point I2 | Measured current at the second point; must exceed I1. |
Choose the inputs correctly
U1 and I1 are voltage and current at the first, lighter-loaded point; U2 and I2 at the second, heavier-loaded point with I2>I1.
How to use the calculator
Set up two stable operating points with clearly different load and measure terminal voltage and current simultaneously at each.
Worked example
U1=12 V at I1=1 A and U2=11 V at I2=6 A give Ri=(12−11)/(6−1)=0.2 Ω.
Understand the result and units
A larger voltage drop between the two points for the same current difference indicates higher internal resistance.
U1 and U2 are voltages, I1 and I2 currents. Ri is output as a resistance.
Typical applications
Characterising batteries, solar cells or power supplies in the field when open-circuit voltage cannot or should not be measured separately.
Assumptions, limits and common mistakes
Linear source model with Ri constant over the measurement range; state-of-charge change during measurement, temperature drift and dynamic behaviour are not included.
Common mistake: Do not choose the two measurement points too close together, since small measurement errors then strongly distort the resulting internal resistance.
Frequently asked questions
What is “Source internal resistance from two load points” used for?
Characterising batteries, solar cells or power supplies in the field when open-circuit voltage cannot or should not be measured separately.
Where do the input values come from?
U1 and I1 are voltage and current at the first, lighter-loaded point; U2 and I2 at the second, heavier-loaded point with I2>I1.
What does the result not cover?
Linear source model with Ri constant over the measurement range; state-of-charge change during measurement, temperature drift and dynamic behaviour are not included.