A-mittarin toiminta

.

Kysymys 1

Mitä kytkennässä tapahtuu, kun mittari kytketään suoraan 6 V akkuun?

Kysymys 2

Tiedetään, että herkän mittalaitteen kytkeminen sarjaan isovirtaisen sähkölaitteen kanssa on huono juttu. Niinpä täytyisi miettiä, mitä muita komponentteja tulisi kytkeä mukaan, jotta voitaisiin rajoittaa kelan läpi menevää virtaa niin, että 1 A virtapiirissä mittari antaisi täyden näyttämän.

Tee virtapiiripiiros, jossa on molemmat lisäkomponentit. Täydennä kytkentä johtimilla valmiiksi niin, että ampeerimittari on kytketty akun ja 6 ohm vastuksen virtapiiriin tämän virtapiirin virran mittaamiseksi.

Kysymys 3

Määrittele mittauksen alue tälle ampeerimittarille.

Kysymys 4

Mitä tapahtuu tämän ampeerimittarin toiminnassa, jos kuvaan merkitty johdin katkeaisi?

Kysymys 5

Mitä tapahtuisi ampeerimittarin toiminnassa, jos vastus irtoaisi liittimestään?

Kysymys 6

Kuvassa on ampeerimittarin virtapiiri, jossa on erikoisrakenteinen valintakytkin. Se kytkee uuden virtapiirin ennen kuin katkaisee entisen (make-before-break -selector):

Tällainen kytkin on välttämätön ampeerimittarin virtapiirissä, kuten edellä nähtiin. Jos tehtäisiin vastaava ampeerimittari normaalilla valintakytkimellä (break-before-make), mittari vahingoittuisi normaalissa käytössä:

Selosta miksi ensimmäinen virtapiiri on superhyvä toiseen verrattuna, ja millainen käyttö johtaisi mittarin vaurioitumiseen jälkimmäisessä kytkennässä.

Kysymys 7

Ihanteellisessa tapauksessa ampeerimittarilla tulisi olla hyvin pieni sisäinen resistanssi tai hyvin suuri sisäinen resistanssi. Selosta miksi näin.

Kysymys 8

Mitkä mittauskoneiston ominaisuudet vaikuttavat mittarin sisäiseen resistanssiin?

Kysymys 9

Usein käytetään sivuvastuksia mittauskytkennän osana. Ne on suunniteltu niin, että jännitehäviö niiden navoissa on hyvin pieni vaikka suurikin mittausvirta kulkee niiden läpi. Mittaamalla sivuvastuksen jännitehäviö, voidaan määrittää mitattavan virran suuruus:

Kuinka suuri on tämän sivuvastuksen resistanssi, kun sivuvastukseen on merkitty seuraavat arvot: 150 A , 50 mV. ?

Kysymys 10

Virtaa mittaavissa sivuvastuksissa on aina neljä liitintä (normaaleissa vastuksissa on vain kaksi):

Selosta, mitä menisi pieleen, jos V-mittari kytkettäisiin suoraan samoihin liittimiin varsinaisen mitattavan virtapiirin johtimien kanssa, kuten tässä:

Kysymys 11

Sivuvastukset on usein tehty massiivisesta metallista. Niiden resistanssi on justeerattu kohdalleen poistamalla ainetta vastusaihiosta, jonka resistanssi on liian pieni kunnes on saatu resistanssi kohdilleen. Tämä tietenkin toimii vain, jos vastuksen resistanssi aluksi on liian pieni. Kuten vanha puuseppävitsi: "Sahasin pöydänjalkaa kahdesti, ja se on silti liian lyhyt!"

Kun sivuvastuksen resistanssi on niin kovin pieni, niin miten vastuksen resistanssi mitataan justeerausta tehdessä? Sivuvastuksen resistanssi on liian pieni tavanomaisella resistanssimittarilla mitattavaksi ja erikoismittalaitteet pienien resistanssien mittaaiseksi (kuten Kelvin silta) ovat kalliita. Jos saisit tehtäväksesi tällaisen sivuvastuksen resistanssin justeeraamisen kohdalleen, ja sinulla olisi käytettävissä vain tavallisia mittareita, niin miten tekisit?

Kysymys 12

Tärkeä vaihe V- tai A-mittarin tekemisessä on mittarin kelan resistanssin määrittäminen. Helpoin tapa tehdä se on käyttää vastuksia, joiden reistanssit ovat standardin mukaisia (tasalukemia). Varsinainen resistanssimääritys tehdään mittaamalla jännitettä tai virtaa.

Ensiksi kytke mitattava mittarin kela, dekadivastus ja DC-sähköläde sarjaan, Säädä dekadivastuksen resistanssi niin, että mittarin neula asettuu haluamaasi kohtaan asteikolla (yleensä maksimilukemaan). Merkitse ylös dekadivastuksen resistanssi arvoksi R1:

Sitten kytke tunnettu vastus mittarin liittimien kanssa rinnan. Tämän vastuksen resistanssi tiedetään ja se on Rs. Mittarin osoitus pienenee jonkin verran, kun teet tämän. Säädä uudelleen dekadin resistanssi, kunnes osoitus on sama kuin aiemmassa mittauksessa. Laita dekadivastuksen täksi arvoksi R2:

Mittarikoneiston kelan resistanssi (Rcoil) voidaan laskea seuraavalla kaavalla:

Tehtävänäsi on osoittaa, miten tämä kaava on saatu. Käytä Ohmin lakia ja muita kaavoja.

Vinkki: molemmissa tapauksissa (dekadivastuksen säätö R1 ja R2) kelaan vaikuttava jännite on yhtä suuri.

Question 13

Don't just sit there! Build something!!

Virtapiirien analysointi vaatii paljon opiskelua ja harjoittelua. Yleensä opiskelijoiden opiskelu on sitä, että tehdään paljon erilaisia tehtäviä ja tarkistetaan niiden vastaukset vastauskirjoista tai opettajalta. Tämä on tietenkin hyvä, mutta on paljon parempikin keino.

Opit paljon enemmän rakentamalla oikean kytkennän ja analysioimalla ja tutkimalla sen antaen oikean virtapiirin antaa vastaukset kysymyksiin kirjan tai opettajan sijasta. Tässä ohjeet sinulle tehokkaaseen opiskeluun:

1. Carefully measure and record all component values prior to circuit construction.

2. Draw the schematic diagram for the circuit to be analyzed.

3. Carefully build this circuit on a breadboard or other convenient medium.

4. Check the accuracy of the circuit's construction, following each wire to each connection point, and

verifying these elements one-by-one on the diagram.

5. Mathematically analyze the circuit, solving for all values of voltage, current, etc.

6. Carefully measure those quantities, to verify the accuracy of your analysis.

7. If there are any substantial errors (greater than a few percent), carefully check your circuit's construction

against the diagram, then carefully re-calculate the values and re-measure.

Avoid very high and very low resistor values, to avoid measurement errors caused by meter "loading".

I recommend resistors between 1 k­ and 100 k­, unless, of course, the purpose of the circuit is to illustrate

the e®ects of meter loading!

One way you can save time and reduce the possibility of error is to begin with a very simple circuit and

incrementally add components to increase its complexity after each analysis, rather than building a whole

new circuit for each practice problem. Another time-saving technique is to re-use the same components in a

variety of di®erent circuit con¯gurations. This way, you won't have to measure any component's value more

than once.

Answers

Answer 1

Two things would happen: ¯rst, the movement would most likely be damaged from excessive current.

Secondly, the needle would move to the left instead of the right (as it normally should), because the polarity

is backward.

Answer 2

Follow-up question: given the 0 to 1 amp range of the ammeter created by the 0.4004 ­ "shunt" resistor,

how much current will the meter actually register when connected in series with the 6 volt battery and 6

ohm resistor? Is this the real current, or is the meter giving us a false indication?

Answer 3

Range = 500 mA

Answer 4

If the wire were to fail open, the ammeter would not respond at all to any amount of input current.

Answer 5

If the resistor were to fail open, the ammeter would become much more sensitive.

Answer 6

The type of use that would damage the second meter but not the ¯rst is changing ranges while measuring

current.

Answer 7

Ideally, an ammeter should have the least amount of input resistance possible. This is important when

using it to measure current in circuits containing little resistance.

Answer 8

To achieve the lowest possible input resistance, without changing the range of the ammeter, you need a

meter movement with a minimum full-scale current rating and a minimum amount of coil resistance.

Challenge question: is it possible to improve the performance of an ammeter's meter movement, as per

the recommendations given here, by adding resistors to it? If so, how?

Answer 9

Metric notation: 333.3 uohm

Scienti¯c notation: 3.333 * 10 exp -4 ohm

Plain decimal notation: 0.0003333 ohm

Answer 10

A two-wire shunt resistor connection will not be as accurate as a four-wire shunt resistor, due to stray

resistance within the bolted connection between the wires and the body of the shunt resistor.

Challenge question: draw a schematic diagram showing all stray resistances within the two-wire shunt

connection circuit, in order to clarify the concept.

Answer 11

Build the ammeter and trim the shunt resistor in-place, with a calibrated amount of current through it.

Answer 12

One place to start from is the voltage divider equation,

applied to each circuit scenario:

Since we know that the meter's voltage is the same in the two scenarios, we may set these equations

equal to each other:

Note: the double-bars in the above equation represent the parallel equivalent of Rcoil and Rs, for which

you will have the substitute the appropriate mathematical expression.

Answer 13

Let the electrons themselves give you the answers to your own "practice problems"!

Notes

Notes 1

When an electromechanical meter movement is overpowered, causing the needle to "slam" all the way

to one extreme end of motion, it is commonly referred to as "pegging" the meter. I've seen meter movements

that have been "pegged" so badly that the needles are bent from hitting the stop!

Based on your students knowledge of meter movement design, ask them to tell you what they think

might become damaged in a severe over-power incident such as this. Tell them to be speci¯c in their answers.

Notes 2

Beginning students sometimes feel "lost" when trying to answer a question like this. They may know

how to apply Ohm's Law to a circuit, but they do not know how to design a circuit that makes use of

Ohm's Law for a speci¯c purpose. If this is the case, you may direct their understanding through a series of

questions such as this:

• • Why does the meter movement "peg" if directly connected to the battery?

  • What type of electrical component could be used to direct current "away" from the movement, without limiting the measured current?

  • How might we connect this component to the meter (series or parallel)? (Draw both con¯gurations and let the student determine for themselves which connection pattern ful¯lls the goal of limiting current to the meter.)

The follow-up question is quite interesting, and causes students to carefully evaluate the performance

of the ammeter they've "created". At root, the problem is similar to that of voltmeter loading, except of

course that we're dealing with ammeters here rather than voltmeters.

Notes 3

Determining the ranges for this ammeter is simply an exercise in Ohm's Law. It is very important that

your students recognize the shunt resistor's value as being in milliohms and not Megaohms! Yes, there is a

di®erence between a lower-case letter "m" and a capital letter "M"!

Notes 4

Some students may think the ammeter will fail to respond at all with an open resistor, because they

associate "open" faults with lack of current, and lack of current with zero response from the meter movement.

Careful examination of the circuit, however, reveals that the exact opposite will happen.

Notes 5

Some students may think the ammeter will fail to respond at all with an open resistor, because they

associate "open" faults with lack of current, and lack of current with zero response from the meter movement.

Careful examination of the circuit, however, reveals that the exact opposite will happen.

Notes 6

Another solution to the break-before-make problem is to use a ring shunt circuit rather than have an

independent range resistor for each current measurement range.

Notes 7

The answer to this question is related to the very important principle of meter loading. Technicians,

especially, have to be very aware of meter loading, and how erroneous measurements may result from it. The

answer is also related to how ammeters are connected with the circuits under test: always in series!

Notes 8

If your students have already studied voltmeter design, you might want to ask them to compare the

(single) design factor in°uencing sensitivity ("ohms-per-volt") in an electromechanical voltmeter with the

two factors listed in the answer to this question. Why is the meter movement coil resistance not a factor

in voltmeter sensitivity, but it is in ammeter sensitivity? Challenge your students with this question, by

having them propose some example voltmeter circuits and ammeter circuits with di®erent coil resistances.

Let them figure out how to set up the problems, rather than you setting up the problems for them!

Some students may suggest that the effective coil resistance of a meter movement may be decreased

with the addition of a shunt resistance inside the movement. If anyone proposes this solution, work through

the calculations of an example ammeter circuit on the whiteboard with the class and see what the effect is!

Notes 9

Ask your students how they think a resistor could be made with such a low resistance (a tiny fraction

of an ohm!). What do they think a shunt resistor would look like in real life? If you happen to have a

shunt resistor available in your classroom, show it to your students after they express their opinions on its

construction.

Notes 10

Though a few fractions of an ohm of "stray" resistance may not seem like much, they are signi¯cant

when contrasted against the already (very) low resistance of the shunt resistor's body.

One of the conceptual di±culties I've encountered with students on numerous occasions is confusion

over how much resistance, voltage, current, etc., constitutes a "signi¯cant" amount. For example, I've had

students tell me that the di®erence between 296,342.5 ohms and 296,370.9 ohms is "really big," when in fact

it is less than ten thousandths of a percent of the base resistance values. Students simply subtract the two

resistances and obtain 28.4 ohms, then think that "28.4" is a signi¯cant quantity because it is comparable

to some of the other values they're used to dealing with (100 ohms, 500 ohms, 1000 ohms, etc.).

Conversely, students may fail to see the signi¯cance of a few hundredths of an ohm of stray resistance

in a shunt resistor circuit, when the entire resistance of the shunt resistor itself is only a few hundredths of

an ohm. What matters most in problems of accuracy is the percentage or error, not the absolute value of

the error itself. This is another practical application of estimating skills, which you should reinforce at every

opportunity.

Notes 11

The answer to this question is deceptively simple, yet extremely practical. Sure, it would be nice to

have the best possible test and calibration equipment available to us at any time in our own laboratory, but

we must be realistic. It is extremely important for your students that they engage in discussion on problems

like this from a practical perspective. It is your task and your privilege as their instructor to bring your

own experience into such discussions and challenge students with realistic obstacles to their (often) idealistic

expectations.

Notes 12

This problem is really nothing more than an exercise in algebra, although it also serves to show how

precision electrical measurements may be obtained by using standard resistors rather than precise voltmeters

or ammeters.

Notes 13

It has been my experience that students require much practice with circuit analysis to become pro¯cient.

To this end, instructors usually provide their students with lots of practice problems to work through, and

provide answers for students to check their work against. While this approach makes students pro¯cient in

circuit theory, it fails to fully educate them.

Students don't just need mathematical practice. They also need real, hands-on practice building circuits

and using test equipment. So, I suggest the following alternative approach: students should build their

own "practice problems" with real components, and try to mathematically predict the various voltage and

current values. This way, the mathematical theory "comes alive," and students gain practical pro¯ciency

they wouldn't gain merely by solving equations.

Another reason for following this method of practice is to teach students scienti¯c method: the process

of testing a hypothesis (in this case, mathematical predictions) by performing a real experiment. Students

will also develop real troubleshooting skills as they occasionally make circuit construction errors.

Spend a few moments of time with your class to review some of the "rules" for building circuits before

they begin. Discuss these issues with your students in the same Socratic manner you would normally discuss

the worksheet questions, rather than simply telling them what they should and should not do. I never

cease to be amazed at how poorly students grasp instructions when presented in a typical lecture (instructor

monologue) format!

A note to those instructors who may complain about the "wasted" time required to have students build

real circuits instead of just mathematically analyzing theoretical circuits:

What is the purpose of students taking your course?

If your students will be working with real circuits, then they should learn on real circuits whenever

possible. If your goal is to educate theoretical physicists, then stick with abstract analysis, by all means!

But most of us plan for our students to do something in the real world with the education we give them.

The "wasted" time spent building real circuits will pay huge dividends when it comes time for them to apply

their knowledge to practical problems.

Furthermore, having students build their own practice problems teaches them how to perform primary

research, thus empowering them to continue their electrical/electronics education autonomously.

In most sciences, realistic experiments are much more di±cult and expensive to set up than electrical

circuits. Nuclear physics, biology, geology, and chemistry professors would just love to be able to have their

students apply advanced mathematics to real experiments posing no safety hazard and costing less than a

textbook. They can't, but you can. Exploit the convenience inherent to your science, and get those students

of yours practicing their math on lots of real circuits!