For the purpose of this section it doesn’t matter how an ammeter actually works. Suffice it to say that a current flows through the ammeter and a needle moves over a scale to indicate the current, or else the current is indicated as numbers in a digital display. In order to measure the current through some element of a circuit, the ammeter is placed, of course, in series with the element. Generally an ammeter has rather a low resistance.
An inexpensive voltmeter is really just an ammeter having rather a high resistance. If you want to measure the potential difference across some circuit element, you place the voltmeter, of course, across that element (i.e. in parallel with it). A small portion of the current through the element is diverted through the meter; the meter measures this current, and, from the known resistance of the meter, the potential difference can be calculated – though in practice nobody does any calculation – the scale is marked in volts. Placing a meter across a circuit element in fact slightly reduces the potential difference across the element – that is, it reduces the very thing you want to measure. But, because a voltmeter typically has a high resistance, this effect is small. There are, of course, modern (and more expensive) voltmeters of a quite different design, which take no current at all, and genuinely measure potential difference, but we are concerned in this section with the commonly-encountered ammeter-turned-voltmeter. It may be noticed that the potentiometer described in the previous section takes no current from the circuit element of interest, and is therefore a true voltmeter.
There are meters known as “multimeters” or “avometers” (for amps, volts and ohms), which can be used as ammeters or as voltmeters, and it is with these that this section is concerned.
A typical inexpensive ammeter gives a full scale deflection (FSD) when a current of 15 mA = 0.015 A flows through it. It can be adapted to measure higher currents by connecting a small resistance (known as a “shunt”) across it.
Let’s suppose, for example, that we have a meter that which shows a FSD when a current of 0.015 A flows through it, and that the resistance of the meter is 10 \(\Omega\). We would like to use the meter to measure currents as high as 0.15 A. What value of shunt resistance shall we put across the meter? Well, when the total current is 0.15 A, we want 0.015 A to flow through the meter (which then shows FSD) and the remainder, 0.135 A, is to flow through the shunt. With a current of 0.015 A flowing through the 10 \(\Omega\) meter, the potential difference across it is 0.15 V. This is also the potential difference across the shunt, and, since the current through the shunt is 0.135 A, the resistance of the shunt must be 1.11 \(\Omega\).
We can also use the meter as a voltmeter. Suppose, for example, that we want to measure voltages (horrible word!) of up to 1.5 V. We place a large resistance R in series with the meter, and then place the meter-plus-series-resistance across the potential difference to measured. The total resistance of meter-plus-series-resistance is (10 + R), and it will show a FSD when the current through it is 0.015 A. We want this to happen when the potential difference across it is 1.5 volts. This 1.5 = 0.015 × (10 + R), and so R = 90 \(\Omega\).