Reading a dial
valeur = divisions luesdivisions totales × calibre
Elec Class
learn electricity hands-on
Lesson · chapter 15 of 15
The voltmeter is connected in parallel, across the component; the ammeter is connected in series, by opening the circuit so that the current flows through it. When you don't know the order of magnitude, start with the highest range, then go down to the one just above the value.
The result is worked out before your eyes, line by line, just like on the board.
1I'm looking for
2I enter the known values
Formula used value = nN · range
3The result
Measured value valeur126 V
On a scale of 100 divisions, on the 300 V range, the needle on division 42 reads 126 V.
The definition, the key points to remember and everyday examples.
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.
To find the flow rate in a pipe, you cut the pipe and insert a water meter: all the water goes through it, just as the current goes through the ammeter in series. To find the pressure, you tap a pressure gauge into the side, without cutting anything, just like the voltmeter in parallel. Where it falls short: a water meter tapped into the side breaks nothing, whereas an ammeter connected in parallel causes a short circuit.
| Quantity | Symbol | Unit |
|---|---|---|
| Shunt resistance | Rs | Ω |
| Ammeter resistance | rA | Ω |
| Full-scale current | i | A |
| Total current to measure | I | A |
| Quantity | Symbol | Unit |
|---|---|---|
| Series multiplier | Radd | Ω |
| Voltmeter resistance | rV | Ω |
| Quantity | Symbol | Unit |
|---|---|---|
| Measured resistance | R | Ω |
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).
Four steps to solve a problem, then an example solved line by line.
Voltage: voltmeter in parallel. Current: ammeter in series. Resistance: ohmmeter with the power off, component isolated.
Estimate the expected value with Ohm's law, then take the range just above it.
Count the divisions under the needle, then calculate value = (n / N) × range, with the unit of the range.
Compare it with the calculated value: a big gap points to a wrong connection or an instrument disturbing the circuit.
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.
In parallel: one probe on each side of the component, without opening the circuit. COM socket on the minus side, V socket on the plus side; the wrong way round, a digital multimeter simply shows a negative value.
Because all the current to be measured has to flow through it: you open the circuit and place it in the branch. Its internal resistance is very low (a few hundredths of an ohm on a multimeter's 10 A range), so it hardly affects the current.
Switch off the power, take the component out of the circuit (at least one lead), turn the selector to Ω and put one probe on each side. Don't hold both ends between your fingers: your body, in parallel, distorts the measurement of high resistances.
The largest value it can measure in the selected position, the full-scale value. On a multimeter's 20 V range, you can read up to 19.99 V; beyond that, the display shows "1" or "OL".
The digital one shows the value directly; the analog meter means reading a scale and converting it with the range, but it shows a changing value better. Both are connected the same way.
Its current circuit is connected in series, like an ammeter, and its voltage circuit in parallel, like a voltmeter. In AC, it directly displays the active power P = U × I × cos φ, not just the product U × I.
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.
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.
From the simplest to the most complete, each problem comes with a step-by-step solution.
Have students measure the same 47 Ω resistor with the voltmeter across the ammeter and resistor, then across the resistor only, calculate U / I in both cases, compare with the color code and explain the difference by the internal resistance of the instruments.
Using Elec Class in class