Voltmeters and Ammeters

Voltmeters and ammeters measure the voltage and current, respectively, of a circuit. Some meters in automobile dashboards, digital cameras, cell phones, and tuner-amplifiers are voltmeters or ammeters.

Voltmeters

A voltmeter is an instrument that measures the difference in electrical potential between two points in an electric circuit. An analog voltmeter moves a pointer across a scale in proportion to the circuit's voltage; a digital voltmeter provides a numerical display. Any measurement that can be converted to voltage can be displayed on a meter that is properly calibrated; such measurements include pressure, temperature, and flow.

Voltmeter

Demonstration voltmeter from a physics class

In order for a voltmeter to measure a device's voltage, it must be connected in parallel to that device . This is necessary because objects in parallel experience the same potential difference.

Voltmeter in Parallel

(a) To measure the potential difference in this series circuit, the voltmeter (V) is placed in parallel with the voltage source or either of the resistors. Note that terminal voltage is measured between points a and b. It is not possible to connect the voltmeter directly across the EMF without including its internal resistance, r. (b) A digital voltmeter in use

Ammeters

An ammeter measures the electric current in a circuit. The name is derived from the name for the SI unit for electric current, amperes (A).

In order for an ammeter to measure a device's current, it must be connected in series to that device . This is necessary because objects in series experience the same current. They must not be connected to a voltage source -- ammeters are designed to work under a minimal burden, (which refers to the voltage drop across the ammeter, typically a small fraction of a volt).

Ammeter in Series

An ammeter (A) is placed in series to measure current. All of the current in this circuit flows through the meter. The ammeter would have the same reading if located between points d and e or between points f and a, as it does in the position shown. (Note that the script capital E stands for EMF, and r stands for the internal resistance of the source of potential difference. )

Galvanometers (Analog Meters)

Analog meters have needles that swivel to point at numbers on a scale, as opposed to digital meters, which have numerical readouts.The heart of most analog meters is a device called a galvanometer, denoted by G. Current flow through a galvanometer, I_G, produces a proportional movement, or deflection, of the needle.

The two crucial characteristics of any galvanometer are its resistance and its current sensitivity. Current sensitivity is the current that gives a full-scale deflection of the galvanometer's needle -- in other words, the maximum current that the instrument can measure. For example, a galvanometer with a current sensitivity of 50 μA has a maximum deflection of its needle when 50 μA flows through it, is at the scale's halfway point when 25 μA flows through it, and so on.

If such a galvanometer has a 25-Ω resistance, then a voltage of only V = IR = (50 μA)(25 Ω) = 1.25 mV produces a full-scale reading. By connecting resistors to this galvanometer in different ways, you can use it as either a voltmeter or ammeter to measure a broad range of voltages or currents.

Galvanometers as Voltmeters

A galvanometer can function as a voltmeter when it is connected in series with a large resistance R. The value of R is determined by the maximum voltage that will be measured. Suppose you want 10 V to produce a full-scale deflection of a voltmeter containing a 25-Ω galvanometer with a 50-μA sensitivity. Then 10 V applied to the meter must produce a current of 50 μA. The total resistance must be:

$R_{tot} = R + r = \frac{V}{I} = \frac{10V}{50\mu A} = 200 k\Omega,$

or:

$R = R_{tot} - r = 200 k\Omega - 25 \Omega \approx 200 k \Omega.$

(R is so large that the galvanometer resistance, r, is nearly negligible. ) Note that 5 V applied to this voltmeter produces a half-scale deflection by sending a 25-μA current through the meter, and so the voltmeter's reading is proportional to voltage, as desired. This voltmeter would not be useful for voltages less than about half a volt, because the meter deflection would be too small to read accurately. For other voltage ranges, other resistances are placed in series with the galvanometer. Many meters allow a choice of scales, which involves switching an appropriate resistance into series with the galvanometer.

Galvanometers as Ammeters

The same galvanometer can also function as an ammeter when it is placed in parallel with a small resistance R, often called the shunt resistance. Since the shunt resistance is small, most of the current passes through it, allowing an ammeter to measure currents much greater than those that would produce a full-scale deflection of the galvanometer.

Suppose, for example, we need an ammeter that gives a full-scale deflection for 1.0 A and that contains the same 25-Ω galvanometer with 50-μA sensitivity. Since R and r are in parallel, the voltage across them is the same.

These IR drops are: IR = I_Gr

so that: $IR = \frac{I_G}{I} = \frac{R}{r}.$

Solving for R, and noting that IG is 50 μA and I is 0.999950 A, we have:

$R = r \frac{I_G}{I} = (25 \Omega) \frac{50 \mu A}{0.999950 A} = 1.25 \times 10^{-3} \Omega.$