The lesson
5.1 The multimeter
Outcome 1 of 6 in domain 5 · Instrumentation and measurement
Voltage, current, resistance, continuity, diode; its limits and its traps.
Understand
On the pack’s blades, 56.3 V. In the charger’s wire, 2.98 A. Across a fuse, 0.3 Ω. Three gestures, and for a hundred and fifty years a single needle movement behind them. To know when the instrument lies, you have to know what it really measures: the needle, current, nothing else; the digital meter, a voltage, and current through the voltage across a shunt. Either way, the probe takes its share of the circuit.
July 1820, Ørsted publishes what he saw in the spring: a compass needle turns near a wire carrying a current. Eight weeks later, in Halle, Johann Schweigger winds the wire in turns around the needle, each turn adds its push, and his multiplier is the first instrument that sees a weak current. The name that stays is galvanometer. For sixty years the magnet moves and the coil stands still: the instrument feels every piece of iron in the room and its deflection does not follow the current. In 1882, Jacques-Arsène d’Arsonval and Marcel Deprez turn the thing around: the magnet is fixed, the wound frame rotates in a gap where the field is the same everywhere, and the mirror, then Weston’s needle in 1888, advances in proportion to the current. It is still the moving coil of every needle instrument.
A moving coil measures only current, and little of it: 50 µA at the end of the scale. Everything else is added resistance. A large resistor in series, so the voltage pushes only those 50 µA through: that is the voltmeter. A small resistor in parallel, a shunt, that lets almost all the current pass beside the coil: that is the ammeter. A battery on top: that is the ohmmeter. In 1923, Donald Macadie, a British Post Office engineer, puts the three in an oak box, the AVO, for amps, volts, ohms. The multimeter is born.
A moving-coil voltmeter therefore draws current from the circuit it measures, and this was stated in ohms per volt: a Simpson 260 at 20,000 Ω/V presents 200 kΩ on its 10 V range. Set on a divider of two 1 MΩ resistors under 12 V, which should give 6 V, it reads 1.7 V, because its 200 kΩ in parallel crush the bottom resistor. Then the Fluke 8020A of 1977, the first successful handheld digital meter, presents a fixed 10 MΩ whatever the range, and on almost everything one measures, 10 MΩ is infinity. Two generations forgot the problem. It comes back the day one reads the 1 MΩ divider through which a BMS watches its cell: 1 MΩ in parallel with 10 MΩ makes 909 kΩ, the reading drops from 6 V to 5.71 V, 4.8% less, and nothing on the display says the instrument changed the circuit.
The same infinity works the other way. A disconnected wire in the shed, in the same conduit as a live one, reads 50 V, sometimes 80, at 10 MΩ: the capacitance between the two wires easily feeds an instrument that asks for nothing. A light bulb in parallel, or the "LoZ" range of a few kilohms, and the ghost voltage falls to zero. The load is the proof.
Current, for its part, is measured in series: the circuit cut and closed again through the instrument, the charger’s 3 A through the 10 A jack. In that jack, the multimeter is nearly a short circuit, by design. Set in parallel across the pack, like a voltmeter, it lets the pack decide the current, hundreds of amperes, for as long as the fuse takes to blow. That is why it is an HRC fuse, sand-filled ceramic, rated 1,000 V, made to quench an arc; a glass fuse of the same amperage in its place is a firecracker held in the hand. The CAT III 600 V on the case says the same thing for mains: a 6,000 V spike coming from a distribution panel does not reach the fingers.
AC remains. An ordinary multimeter rectifies the signal, takes its average and multiplies by 1.11, the ratio that is right for a sine wave alone; on a square wave, it reads 11 % too high. "True RMS" means the instrument squares before averaging, and the figure means something on any shape, within its bandwidth and up to a crest factor of three. The chopped signal of a motor controller, at 8 or 20 kHz, escapes both: the AC range is AC-coupled and specified up to one kilohertz, and each shows a figure that changes with the duty cycle without being the RMS. There, it is the oscilloscope.
The classic mistake: believing the display because it is digital. Four digits state the resolution, not that the probe left the circuit untouched.
What the source lacks
The LoZ range and the ghost voltage. Kuphaldt treats high impedance as a virtue; he does not say that a dead wire can read 50 V because of it, nor that a range of a few kilohms exists to settle the matter.
The measurement category and the HRC fuse. Nothing in him on CAT II, III, IV, nor on what separates the 15 fuse from the 0.50 glass fuse: the breaking capacity, what it can quench without bursting.
True RMS in front of a controller. His chapter is DC; average rectification and its 1.11 factor are in volume II, never in front of pulse-width modulation.
See
Coming: the divider of two 1 MΩ resistors under 12 V, drawn twice, without the voltmeter and with its 10 MΩ in parallel across the bottom resistor, and the two readings, 6.00 V and 5.71 V.
The targets
- The five measurements. DC and AC voltage, resistance, continuity, diode drop, the jack and the range named before the probe is set: 56 V on the blades, 120 V at the outlet, 0.6 V across a diode, a beep on a wire.
- Current in series, and the fuse. The charger’s 3 A read through the 10 A jack, the circuit opened to put the instrument in; then say, without doing it, what happens if the same probe touches the pack in parallel.
- Input impedance. The 1 MΩ / 1 MΩ divider under 12 V, calculated at 6 V, read at 5.71 V; the 1 MΩ ∥ 10 MΩ calculation that explains it, then the reading with two multimeters in parallel, lower still.
- True RMS. The 11% too high on a square wave, calculated then read, with two instruments of which only one is true RMS.
- The clamp and the non-contact tester. The current of one wire at the clamp, and why the clamp around the whole cord reads zero; the non-contact tester that beeps on one wire and not the other, and what it does not see.
- Diagnosis. The shed wire that reads 50 V disconnected: name the parasitic capacitance, apply a bulb or the LoZ range, show the zero.
Misconceptions
"The voltmeter changes nothing in the circuit."
It puts 10 MΩ in parallel. On a 1 MΩ divider, that is 4.8% less; on a 10 MΩ divider, a third less. The rule: above one hundredth of the multimeter’s resistance, calculate before believing."10 A is 10 A."
Two 10 A fuses differ in what they can quench. The multimeter’s is rated 1,000 V and more than ten kiloamperes of breaking capacity; a glass fuse breaks a few tens of amperes and bursts beyond. Swapping it keeps the number and loses the protection."There are 50 V on this wire, it is live."
At 10 MΩ, 50 V is 5 µA, which a parasitic capacitance supplies with ease. A load decides: the voltage holds under a bulb, the wire is live; it falls, it was a ghost.
The word
GalvanometerGalvanomètre
Luigi Galvani, Bologna, 1791: frog legs that twitch between two metals, and the conviction that an animal electricity lives in them. Volta shows it is the metal, and the battery comes out of it. Galvani’s name nonetheless stays on the instrument that measures Volta’s current: Schweigger calls his a "multiplier", and it is Ampère, who put into equations what Ørsted had seen, who proposes "galvanometer" in his 1820 memoir. In French, galvanomètre, the same word; the moving coil is a meter movement, the clockmakers’ "movement".
Read
Kuphaldt, Lessons in Electric Circuits, volume I (DC), chapter 8: DC metering circuits. "What is a meter?" and "Voltmeter design" for the moving coil and the series resistor; "Voltmeter impact on measured circuit" for ohms per volt, with a loaded divider; "Ammeter design" and "Ammeter impact on measured circuit" for the shunt and for the clamp; "Ohmmeter design" for the battery inside and the rule that follows, never on a live circuit; "High voltage ohmmeters" for the megohmmeter; "Multimeters" for the box that holds it all. He writes for the needle; all of it holds for the digital one, whose input is a fixed resistance.
Bridges
- History
- From Ørsted’s compass to d’Arsonval’s moving coil, sixty-two years for a needle to follow the current straight, Galvanometer.
- Physics
- Two wires in a conduit make a capacitor of a few hundred picofarads, enough at 60 Hz for a 10 MΩ voltmeter, Parasitic capacitance.
- Mathematics
- The RMS value is the root of the mean of the squares; it is the peak over √2 for a sine wave and the peak itself for a square wave, Root mean square.
- Building electrical
- A fuse’s breaking capacity, the current it can interrupt without bursting, is what separates the multimeter’s fuse from an automotive one, Fuse (electrical).
What it unlocks
What next?
- 5.2 The oscilloscope: the shape the multimeter sums up in one number, and a 10 MΩ probe as well.
- 1.4 Series, parallel, mixed: the divider the voltmeter loads, and the R ∥ 10 MΩ calculation.
- Why does a contact get hot?: the millivolt measurement under load, where the unloaded ohmmeter sees nothing.
- A bench entry to write: the 1 MΩ divider read with two multimeters.