How does a multimeter measure resistance? A lot of online answers suggest that a constant current stimulus is used. I looked into it and found that the stimulus current is not constant at all for digital multimeter. Perhaps it was true back in the analog meter days. The digital multimeter uses a constant voltage with a resistor in series. For different measurement range, different resistor value is used, large resistor value for large measurement range. Some meters also change the constant voltage for different ranges, normally large voltage at lower resistance range. The series resistor and the resistor under measurement form a resistor divider. The resistance measurement is calculated from the divider voltage.
It is fairly easy to find out the stimulus voltage. First set the ohm meter to manual range. Use a volt meter to measure the voltages of the ohm meter for two known resistance. From the two equations, we can solve the stimulus voltage and the series resistance.
For Fluke 87, the stimulus voltage is 1.235V, the series resistances over the ranges are 6.5K (400-Ohm), 15.7K (4K-Ohm), 106K (40K-Ohm), 1.02M (400K-Ohm), 10M (4M-Ohm) and 10M (40M-Ohm).
For Cen-Tech multimeter, the stimulus is 3V for 200-Ohm range and 0.3V for others. The series resistance is 1.59K (200-Ohm), 3.34K (2K-Ohm), 12.5K (20K-Ohm), 103K (200K-Ohm), and 1M (2M-Ohm).
For high-end digital multimeters, like Keysight 34401A (6.5-digit), it uses current source, 1mA (100 and 1K-Ohm), 100uA (10K), 10uA (100K), 5uA (1M), 0.5uA (10M), 0.5uA||10MOhm (100M).
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