DC Voltmeters and Ammeters

Voltmeters measure voltage, whereas ammeters measure current. Some of the meters in automobile dashboards, digital cameras, cell phones, and tuner-amplifiers are voltmeters or ammeters. (See [link].) The internal construction of the simplest of these meters and how they are connected to the system they monitor give further insight into applications of series and parallel connections.

This photograph shows the instruments on a gray Volkswagen Vento dashboard, including the speedometer, odometer, and fuel and temperature gauges, showing some readings.

Voltmeters are connected in parallel with whatever device’s voltage is to be measured. A parallel connection is used because objects in parallel experience the same potential difference. (See [link], where the voltmeter is represented by the symbol V.)

Ammeters are connected in series with whatever device’s current is to be measured. A series connection is used because objects in series have the same current passing through them. (See [link], where the ammeter is represented by the symbol A.)

Part a shows a schematic drawing of a circuit with a voltage source and its internal resistance, in series with two load resistors R sub one and R sub two having two probes of a voltmeter connected in parallel with each component. There is another resistor in series to close the circuit. Part b shows a photograph of a black voltmeter connected to two inputs on an electrical device, with a digital readout of the voltage across the source as an L E D display.

The diagram of an electric circuit shows a voltage source of e m f script E and internal resistance r and two resistive loads R sub one and R sub two. All are connected in series with an ammeter A.

Analog Meters: Galvanometers

Analog meters have a needle that swivels to point at numbers on a scale, as opposed to digital meters, which have numerical readouts similar to a hand-held calculator. The heart of most analog meters is a device called a galvanometer, denoted by G. Current flow through a galvanometer, IG size 12{I rSub { size 8{G} } } {}

, produces a proportional needle deflection. (This deflection is due to the force of a magnetic field upon a current-carrying wire.)

The two crucial characteristics of a given galvanometer are its resistance and current sensitivity. Current sensitivity is the current that gives a full-scale deflection of the galvanometer’s needle, 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, reads half-scale when 25 μA size 12{2"5 "μA} {}

flows through it, and so on.

If such a galvanometer has a 25-Ω size 12{2"5-" %OMEGA } {}

resistance, then a voltage of only V=IR=50 μA25 Ω=1.25 mV size 12{V= ital "IR"= left ("50" μA right ) left ("25" %OMEGA right )=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 that can measure a broad range of voltages or currents.

Galvanometer as Voltmeter

[link] shows how a galvanometer can be used as a voltmeter by connecting it in series with a large resistance, R

. The value of the resistance R size 12{R} {}

is determined by the maximum voltage to be measured. Suppose you want 10 V to produce a full-scale deflection of a voltmeter containing a 25-Ω size 12{2"5-" %OMEGA } {}

galvanometer with a 50-μA

sensitivity. Then 10 V applied to the meter must produce a current of 50 μA size 12{"50" μA} {}

. The total resistance must be

Rtot=R+r=VI=10 V50 μA=200 kΩ, or size 12{R rSub { size 8{"tot"} } =R+r= { {V} over {I} } = { {"10"" V"} over {"50" μA} } ="200"" k" %OMEGA } {}
R=Rtot−r=200 kΩ−25Ω≈200 kΩ. size 12{R=R rSub { size 8{"tot"} } -r="200"k %OMEGA -"25" %OMEGA »"200"" k" %OMEGA } {}

(R size 12{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 producing a 25-μA size 12{2"5-"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 small and difficult to read accurately. For other voltage ranges, other resistances are placed in series with the galvanometer. Many meters have a choice of scales. That choice involves switching an appropriate resistance into series with the galvanometer.

The drawing shows a voltmeter, which is a circuit with a large resistance in series with a galvanometer, along with its internal resistance.

Galvanometer as Ammeter

The same galvanometer can also be made into an ammeter by placing it in parallel with a small resistance R size 12{R} {}

, often called the shunt resistance, as shown in [link]. Since the shunt resistance is small, most of the current passes through it, allowing an ammeter to measure currents much greater than those producing a full-scale deflection of the galvanometer.

Suppose, for example, an ammeter is needed that gives a full-scale deflection for 1.0 A, and contains the same 25-Ω size 12{2"5-" %OMEGA } {}

galvanometer with its 50-μA size 12{"50"-μA} {}

sensitivity. Since R size 12{R} {}

and r size 12{r} {}

are in parallel, the voltage across them is the same.

These IR size 12{ ital "IR"} {}

drops are IR=IGr size 12{ ital "IR"=I rSub { size 8{G} } r} {}

so that IR=IGI=Rr size 12{ ital "IR"= { {I rSub { size 8{G} } } over {I} } = { {R} over {r} } } {}

. Solving for R size 12{R} {}

, and noting that IG size 12{I rSub { size 8{G} } } {}

is 50 μA size 12{"50" μA} {}

and I size 12{I} {}

is 0.999950 A, we have

R=rIGI=(25Ω)50 μA0.999950 A=1.25×10−3Ω. size 12{R=r { {I rSub { size 8{G} } } over {I} } = \( "25" %OMEGA \) { {"50" mA} over {0 "." "999950 A"} } =1 "." "25"´"10" rSup { size 8{-3} } %OMEGA } {}

A resistance R is placed in parallel with a galvanometer G having an internal resistance r to produce an ammeter.

Taking Measurements Alters the Circuit

When you use a voltmeter or ammeter, you are connecting another resistor to an existing circuit and, thus, altering the circuit. Ideally, voltmeters and ammeters do not appreciably affect the circuit, but it is instructive to examine the circumstances under which they do or do not interfere.

First, consider the voltmeter, which is always placed in parallel with the device being measured. Very little current flows through the voltmeter if its resistance is a few orders of magnitude greater than the device, and so the circuit is not appreciably affected. (See [link](a).) (A large resistance in parallel with a small one has a combined resistance essentially equal to the small one.) If, however, the voltmeter’s resistance is comparable to that of the device being measured, then the two in parallel have a smaller resistance, appreciably affecting the circuit. (See [link](b).) The voltage across the device is not the same as when the voltmeter is out of the circuit.

Part a shows a desired case in which the resistance of a voltmeter connected in parallel with a load resistor is essentially equivalent to the resistance of the load resistor along as long as the voltmeter’s resistance is much greater than that of the load resistor. Part b shows the case when the voltmeter’s resistance is approximately the same as that of the load resistor. This case should be avoided because the effective resistance is half that of the load resistor.

An ammeter is placed in series in the branch of the circuit being measured, so that its resistance adds to that branch. Normally, the ammeter’s resistance is very small compared with the resistances of the devices in the circuit, and so the extra resistance is negligible. (See [link](a).) However, if very small load resistances are involved, or if the ammeter is not as low in resistance as it should be, then the total series resistance is significantly greater, and the current in the branch being measured is reduced. (See [link](b).)

A practical problem can occur if the ammeter is connected incorrectly. If it was put in parallel with the resistor to measure the current in it, you could possibly damage the meter; the low resistance of the ammeter would allow most of the current in the circuit to go through the galvanometer, and this current would be larger since the effective resistance is smaller.

The figure shows two cases in which an ammeter is connected in series with a load resistor. Part a shows the desired case in which the resistance of the ammeter is much smaller than that of the load, and the total resistance is about the same as the load resistance. Part b shows the case to be avoided in which the ammeter has a resistance about the same as the load, and the total resistance is twice that of the load resistance.

One solution to the problem of voltmeters and ammeters interfering with the circuits being measured is to use galvanometers with greater sensitivity. This allows construction of voltmeters with greater resistance and ammeters with smaller resistance than when less sensitive galvanometers are used.

There are practical limits to galvanometer sensitivity, but it is possible to get analog meters that make measurements accurate to a few percent. Note that the inaccuracy comes from altering the circuit, not from a fault in the meter.

Connections: Limits to Knowledge

Making a measurement alters the system being measured in a manner that produces uncertainty in the measurement. For macroscopic systems, such as the circuits discussed in this module, the alteration can usually be made negligibly small, but it cannot be eliminated entirely. For submicroscopic systems, such as atoms, nuclei, and smaller particles, measurement alters the system in a manner that cannot be made arbitrarily small. This actually limits knowledge of the system—even limiting what nature can know about itself. We shall see profound implications of this when the Heisenberg uncertainty principle is discussed in the modules on quantum mechanics.

There is another measurement technique based on drawing no current at all and, hence, not altering the circuit at all. These are called null measurements and are the topic of Null Measurements. Digital meters that employ solid-state electronics and null measurements can attain accuracies of one part in 106 size 12{"10" rSup { size 8{6} } } {}

.

Check Your Understanding

Digital meters are able to detect smaller currents than analog meters employing galvanometers. How does this explain their ability to measure voltage and current more accurately than analog meters?

Since digital meters require less current than analog meters, they alter the circuit less than analog meters. Their resistance as a voltmeter can be far greater than an analog meter, and their resistance as an ammeter can be far less than an analog meter. Consult [link] and [link] and their discussion in the text.

PhET Explorations: Circuit Construction Kit (DC Only), Virtual Lab

Stimulate a neuron and monitor what happens. Pause, rewind, and move forward in time in order to observe the ions as they move across the neuron membrane.

[Circuit Construction Kit (DC Only), Virtual Lab](circuit-construction-kit-dc-virtual-lab_en.jar)

Section Summary

Conceptual Questions

Why should you not connect an ammeter directly across a voltage source as shown in [link]? (Note that script E in the figure stands for emf.)

A circuit shows a connection of a cell of e m f script E and internal resistance r. Each terminal of the cell is connected to opposite ends of the ammeter. The circuit is closed.

Suppose you are using a multimeter (one designed to measure a range of voltages, currents, and resistances) to measure current in a circuit and you inadvertently leave it in a voltmeter mode. What effect will the meter have on the circuit? What would happen if you were measuring voltage but accidentally put the meter in the ammeter mode?

Specify the points to which you could connect a voltmeter to measure the following potential differences in [link]: (a) the potential difference of the voltage source; (b) the potential difference across R1 size 12{R rSub { size 8{1} } } {}

; (c) across R2 size 12{R rSub { size 8{2} } } {}

; (d) across R3 size 12{R rSub { size 8{3} } } {}

; (e) across R2 size 12{R rSub { size 8{2} } } {}

and R3 size 12{R rSub { size 8{3} } } {}

. Note that there may be more than one answer to each part.

This figure shows a circuit having a cell of e m f script E and internal resistance r connected in parallel to two arms, one arm containing resistor R sub one and a second arm containing a series of resistors R sub two and R sub three.

To measure currents in [link], you would replace a wire between two points with an ammeter. Specify the points between which you would place an ammeter to measure the following: (a) the total current; (b) the current flowing through R1 size 12{R rSub { size 8{1} } } {}

; (c) through R2 size 12{R rSub { size 8{2} } } {}

; (d) through R3 size 12{R rSub { size 8{3} } } {}

. Note that there may be more than one answer to each part.

Problem Exercises

What is the sensitivity of the galvanometer (that is, what current gives a full-scale deflection) inside a voltmeter that has a 1.00-MΩ size 12{1 "." "00""-M" %OMEGA } {}

resistance on its 30.0-V scale?

30 μA size 12{"30" μA} {}

What is the sensitivity of the galvanometer (that is, what current gives a full-scale deflection) inside a voltmeter that has a 25.0-kΩ size 12{"25" "." 0"-k" %OMEGA } {}

resistance on its 100-V scale?

Find the resistance that must be placed in series with a 25.0-Ω size 12{"25" "." 0- %OMEGA } {}

galvanometer having a 50.0-μA size 12{"50" "." 0-μA} {}

sensitivity (the same as the one discussed in the text) to allow it to be used as a voltmeter with a 0.100-V full-scale reading.

1 . 98 k Ω size 12{1 "." "98 k" %OMEGA } {}

Find the resistance that must be placed in series with a 25.0-Ω size 12{"25" "." 0- %OMEGA } {}

galvanometer having a 50.0-μA size 12{"50" "." 0-μA} {}

sensitivity (the same as the one discussed in the text) to allow it to be used as a voltmeter with a 3000-V full-scale reading. Include a circuit diagram with your solution.

Find the resistance that must be placed in parallel with a 25.0-Ω size 12{"25" "." 0- %OMEGA } {}

galvanometer having a 50.0-μA size 12{"50" "." 0-μA} {}

sensitivity (the same as the one discussed in the text) to allow it to be used as an ammeter with a 10.0-A full-scale reading. Include a circuit diagram with your solution.

1 . 25 × 10 - 4 Ω size 12{1 "." "25"´"10" rSup { size 8{ +- 4} } %OMEGA } {}

Find the resistance that must be placed in parallel with a 25.0-Ω size 12{"25" "." 0- %OMEGA } {}

galvanometer having a 50.0-μA size 12{"50" "." 0-μA} {}

sensitivity (the same as the one discussed in the text) to allow it to be used as an ammeter with a 300-mA full-scale reading.

Find the resistance that must be placed in series with a 10.0-Ω size 12{"10" "." 0- %OMEGA } {}

galvanometer having a 100-μA size 12{"100"-μA} {}

sensitivity to allow it to be used as a voltmeter with: (a) a 300-V full-scale reading, and (b) a 0.300-V full-scale reading.

(a) 3.00 MΩ size 12{3 "." "00 M" %OMEGA } {}

(b) 2.99 kΩ size 12{2 "." "99 k" %OMEGA } {}

Find the resistance that must be placed in parallel with a 10.0-Ω size 12{"10" "." 0- %OMEGA } {}

galvanometer having a 100-μA size 12{"100"-μA} {}

sensitivity to allow it to be used as an ammeter with: (a) a 20.0-A full-scale reading, and (b) a 100-mA full-scale reading.

Suppose you measure the terminal voltage of a 1.585-V alkaline cell having an internal resistance of 0.100Ω size 12{0 "." "100" %OMEGA } {}

by placing a 1.00-kΩ size 12{1 "." "00""-k" %OMEGA } {}

voltmeter across its terminals. (See [link].) (a) What current flows? (b) Find the terminal voltage. (c) To see how close the measured terminal voltage is to the emf, calculate their ratio.

The figure shows a circuit diagram that includes a battery with an internal resistance r and a voltmeter connected across its terminals. The current I is shown by an arrow pointing in a clockwise direction.

(a) 1.58 mA

(b) 1.5848 V (need four digits to see the difference)

(c) 0.99990 (need five digits to see the difference from unity)

Suppose you measure the terminal voltage of a 3.200-V lithium cell having an internal resistance of 5.00Ω size 12{5 "." "00" %OMEGA } {}

by placing a 1.00-kΩ size 12{1 "." "00""-k" %OMEGA } {}

voltmeter across its terminals. (a) What current flows? (b) Find the terminal voltage. (c) To see how close the measured terminal voltage is to the emf, calculate their ratio.

A certain ammeter has a resistance of 5.00×10−5Ω size 12{5 "." "00"´"10" rSup { size 8{-5} } %OMEGA } {}

on its 3.00-A scale and contains a 10.0-Ω size 12{"10" "." 0- %OMEGA } {}

galvanometer. What is the sensitivity of the galvanometer?

15 . 0 μA size 12{"15" "." 0 mA} {}

A 1.00-MΩ size 12{1 "." "00""-M" %OMEGA } {}

voltmeter is placed in parallel with a 75.0-kΩ size 12{"75" "." 0"-k" %OMEGA } {}

resistor in a circuit. (a) Draw a circuit diagram of the connection. (b) What is the resistance of the combination? (c) If the voltage across the combination is kept the same as it was across the 75.0-kΩ size 12{"75" "." 0"-k" %OMEGA } {}

resistor alone, what is the percent increase in current? (d) If the current through the combination is kept the same as it was through the 75.0-kΩ size 12{"75" "." 0"-k" %OMEGA } {}

resistor alone, what is the percentage decrease in voltage? (e) Are the changes found in parts (c) and (d) significant? Discuss.

A 0.0200-Ω

ammeter is placed in series with a 10.00-Ω size 12{"10" "." "00"- %OMEGA } {}

resistor in a circuit. (a) Draw a circuit diagram of the connection. (b) Calculate the resistance of the combination. (c) If the voltage is kept the same across the combination as it was through the 10.00-Ω size 12{"10" "." "00"- %OMEGA } {}

resistor alone, what is the percent decrease in current? (d) If the current is kept the same through the combination as it was through the 10.00-Ω size 12{"10" "." "00"- %OMEGA } {}

resistor alone, what is the percent increase in voltage? (e) Are the changes found in parts (c) and (d) significant? Discuss.

(a)

The figure shows part of a circuit that includes an ammeter with internal resistance r connected in series with a load resistance R.

(b) 10.02 Ω size 12{10 "." "02 " %OMEGA } {}

(c) 0.9980, or a 2.0×10–1

percent decrease

(d) 1.002, or a 2.0×10–1

percent increase

(e) Not significant.

Unreasonable Results

Suppose you have a 40.0-Ω size 12{"40" "." 0- %OMEGA } {}

galvanometer with a 25.0-μA size 12{"25" "." 0-mA} {}

sensitivity. (a) What resistance would you put in series with it to allow it to be used as a voltmeter that has a full-scale deflection for 0.500 mV? (b) What is unreasonable about this result? (c) Which assumptions are responsible?

Unreasonable Results

(a) What resistance would you put in parallel with a 40.0-Ω size 12{"40" "." 0- %OMEGA } {}

galvanometer having a 25.0-μA

sensitivity to allow it to be used as an ammeter that has a full-scale deflection for 10.0-μA size 12{"10" "." 0 μA} {}

? (b) What is unreasonable about this result? (c) Which assumptions are responsible?

(a) −66.7Ω size 12{-"66" "." 7 %OMEGA } {}

(b) You can’t have negative resistance.

(c) It is unreasonable that IG size 12{I rSub { size 8{G} } } {}

is greater than Itot size 12{I rSub { size 8{"tot"} } } {}

(see [link]). You cannot achieve a full-scale deflection using a current less than the sensitivity of the galvanometer.

Glossary

voltmeter
an instrument that measures voltage
ammeter
an instrument that measures current
analog meter
a measuring instrument that gives a readout in the form of a needle movement over a marked gauge
digital meter
a measuring instrument that gives a readout in a digital form
galvanometer
an analog measuring device, denoted by G, that measures current flow using a needle deflection caused by a magnetic field force acting upon a current-carrying wire
current sensitivity
the maximum current that a galvanometer can read
full-scale deflection
the maximum deflection of a galvanometer needle, also known as current sensitivity; a galvanometer with a full-scale deflection of 50 μA size 12{"50" mA} {}

has a maximum deflection of its needle when

50 μA size 12{"50" μA} {}

flows through it

shunt resistance
a small resistance R size 12{R} {}

placed in parallel with a galvanometer G to produce an ammeter; the larger the current to be measured, the smaller

R size 12{R} {}

must be; most of the current flowing through the meter is shunted through

R size 12{R} {}

to protect the galvanometer

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