Calculator
Formula Used
The calculator first corrects amplifier readings:
Corrected voltage = (Amplifier reading − Offset) ÷ Gain
Then it applies the loaded source method:
Internal resistance = Load resistance × ((Open voltage ÷ Loaded voltage) − 1)
The load path can include lead resistance and temperature correction:
Corrected load = Nominal load × (1 + TCR × ΔT ÷ 1,000,000) + Lead resistance
How to Use This Calculator
- Measure the amplifier output with no load connected.
- Connect a known load resistor and measure again.
- Enter amplifier gain and zero offset.
- Enter the load value, lead resistance, and temperature data.
- Add uncertainty values if you want an error estimate.
- Press Calculate to show results above the form.
- Use CSV or PDF buttons to save the report.
Example Data Table
| Case | Open Reading | Loaded Reading | Gain | Load | Estimated Internal Resistance |
|---|---|---|---|---|---|
| Small signal source | 2.500 V | 2.250 V | 10 | 100 ohm | 11.11 ohm |
| Battery test | 12.600 V | 12.200 V | 1 | 20 ohm | 0.656 ohm |
| Sensor output | 800 mV | 760 mV | 5 | 10 kilo ohm | 526.3 ohm |
Internal Resistance With Amplifier Measurements
Internal resistance shows how much a source sags when it supplies current. A perfect source would hold the same voltage under every load. Real cells, sensors, generators, and signal sources do not. Their terminal voltage falls because part of the voltage is lost inside the source.
Amplifiers help when the source voltage is small. They scale microvolt or millivolt readings into a cleaner range. The calculator corrects those readings by gain and zero offset before using the resistance formula. This makes the result closer to the real source value.
Measurement Method
The open circuit reading is taken with almost no load. It represents the Thevenin voltage after correction. The loaded reading is taken with a known resistor connected. The load creates current. The voltage drop between the two corrected readings reveals the hidden internal resistance.
Use a load resistor that is stable and rated for the expected power. A very small resistor may heat up. A very large resistor may create too little voltage change. Both cases can reduce accuracy. The tool includes lead resistance and temperature coefficient corrections, so lab data can be compared more fairly.
Amplifier Corrections
A measurement amplifier has gain. It may also have offset. The real voltage equals the displayed amplifier reading minus offset, divided by gain. Enter the same gain and offset used during both readings. Keep units consistent. If the amplifier clips, saturates, or drifts during the test, repeat the measurement.
The uncertainty fields give a practical error estimate. They combine voltage reading error and load resistor tolerance. This does not replace full calibration, but it gives a useful planning value. It helps decide if the measured resistance is meaningful.
Practical Uses
This calculator is useful for battery checks, sensor output testing, audio source analysis, and lab supply evaluation. It can also estimate output resistance before matching stages. The CSV option stores numeric results. The PDF option creates a simple report. Use the result with safety limits, component ratings, and normal engineering judgment.
Good Practice
Record the meter range, amplifier model, load value, and ambient temperature. Let parts settle before reading. Take several readings, average stable values, and reject results taken during warm up or obvious electrical noise.
FAQs
1. What is internal resistance?
Internal resistance is the hidden resistance inside a real voltage source. It causes terminal voltage to drop when current flows through a connected load.
2. Why use an amplifier for this test?
An amplifier makes small voltage changes easier to measure. The calculator removes gain and offset effects before calculating resistance.
3. Which load resistor should I choose?
Choose a stable resistor that creates a clear voltage drop without overheating the source or resistor. Avoid extreme load values.
4. What does amplifier offset mean?
Offset is the reading shown when the real input should be zero. Subtracting it improves low voltage measurement accuracy.
5. Can the result be negative?
Yes. A negative result can happen because of noise, active regulation, wrong polarity, unstable loading, or a clipped amplifier reading.
6. What is expanded uncertainty?
Expanded uncertainty is twice the standard uncertainty here. It gives a wider practical range for the estimated internal resistance.
7. Does lead resistance matter?
Lead resistance matters when the load is small or current is high. Enter it to correct the effective load path.
8. Can I use this for batteries?
Yes. Use suitable loads, short test times, and safe current limits. Batteries can heat or sag during heavy loading.