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Reminder sheet

Measurement & instruments

Bastaya

A good instrument, badly connected, lies. Voltmeter in parallel, ammeter in series, ohmmeter with the power off: three rules to engrave on your shield.

The voltmeter is connected in parallel (very large internal resistance); the ammeter in series (very small internal resistance); the ohmmeter on a de-energised circuit; the wattmeter has a current coil in series and a voltage coil in parallel.

Choose the range just above the expected value for a precise reading. Internal resistances slightly bias the measurement: the downstream connection suits small resistances, the upstream one large resistances. A parallel shunt extends the range of an ammeter.

Formulas

Reading a dialvaleur = divisions luesdivisions totales × calibre
Ammeter shuntRs = rA · iI − i
QuantitySymbolUnit
Shunt resistanceRsΩ
Ammeter resistancerAΩ
Full-scale currentiA
Total current to measureIA
Series multiplier (voltmeter)Radd = Ui − rV
QuantitySymbolUnit
Series multiplierRaddΩ
Voltmeter resistancerVΩ
Volt-ammeter methodR = UI
QuantitySymbolUnit
Measured resistanceRΩ

Downstream: the voltmeter is across R alone (error from the current shunted by V); upstream: the voltmeter spans A (error from the drop in A).

Worked example

An ammeter of internal resistance r_A = 0.1 Ω has a 1 A range. What shunt lets it measure up to 10 A? A dial voltmeter with 100 divisions on the 300 V range, needle on division 42: what voltage?

At 10 A the instrument must only receive i = 1 A: the shunt diverts I − i = 9 A.

R_s = r_A · i / (I − i) = 0.1 × 1 / 9 = 0.011 Ω (11 mΩ), in parallel with the ammeter.

Dial reading: U = (42 / 100) × 300 = 126 V.

Common mistakes

  • Connecting the ammeter in parallel: its near-zero resistance makes a short circuit, the fuse blows. It goes in series, in the branch.
  • Choosing a range too small (needle at full scale, damaged instrument) or too large (imprecise reading): the range just above the expected value.
  • Measuring a resistance with an ohmmeter in a live circuit: the reading is wrong and the instrument may burn out. Power off, component isolated.

IEC symbols

VVoltmeter
AAmmeter
ΩOhmmeter
WWattmeter

Mini circuit

Open in the sandbox

Frequently asked questions

Downstream or upstream connection to measure a resistance?
Downstream (voltmeter directly across R) for small resistances: the current drawn by the voltmeter is then negligible. Upstream (voltmeter also across the ammeter) for large ones: the drop in the ammeter is then negligible.
Why choose the range just above the expected value?
The uncertainty of an instrument is a percentage of the range, not of the reading: 1 % of 300 V is 3 V whether you measure 30 V or 280 V. The further the needle along the scale, the more precise the measurement.

15 exercises in this topic

This chapter is covered by the paths: Discovery, General electricity, Measurement prep

All sheets · All formulas · Glossary of electrical quantities · Standard electrical symbols (IEC 60617)

Practise this topic
Simulated time00:00:00
Q = I·t-
W = P·t-

Workbench

Circuit diagram CEI 60617

How does it work?

The perfboard: each big hole is a circuit node. You push a single leg of a component (resistor, lamp...) into it. The 4 small holes around it are connected to it: that is where chips and leads plug in.

  1. Drag a component onto the board: it snaps onto the grid. R rotates it.
  2. To join neighbouring big holes, click Jumper chip in the palette (or C) then drag on the board: a line of chips is laid at once. Bridged holes become a single node.
  3. For long links and for the power supply (placed next to the board), drag a lead from one big hole to another (or to a terminal).
  4. As soon as a loop is closed, the circuit is solved in real time (Ohm + Kirchhoff) and the diagram follows.
  5. Zoom with the wheel (or + / −, two-finger pinch); drag the background to pan, 0 fits the board. The + buttons around the board add a row or a column.

Del delete · R rotate · C chip brush · Esc cancel · wheel zoom · drag the background to pan

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