Съдържание

Условие Task 1 (3 т.)Task 2 (5 т.)Task 3 (2 т.)Answer sheet Topic was proposed by Решение

RMPh 2014, Експеримент — Задача 2. Electrical Black Box

Оригинал на условието (PDF)Съобщи за грешка

Всички материали от RMPh 2014

Experimental Problems — chronometer and electrical black box · 10 т.

Внимание: Бележка към темата

Two independent ten-point experiments with six connected tasks and 26 printed Parts; catalogue 29differs from native source. All 26 primary question/form pages,13 matching Romanian key pages and 26additional English question/form pages were obtained and read. The two English originals repeat the same complete tasks and all 21blank form pages; PDF/font encoding and image bytes differ. Both original citations are retained without a duplicate entry. The supplied official key is preserved in Romanian; no English key was obtained. No time limit is printed. Physical apparatus and marked paper described by the question are not invented as digital companions. Printed scientific/notation/reference errors are retained and disclosed below.

Source editions and literal discrepancies

Romanian Master of Physics 2014. The primary English question/form original and the additional English question/form original contain the same two complete ten-point experiments. Both sources remain cited. The matching supplied “Barem de evaluare şi de notare” is Romanian and accepts any other correct method; it is transcribed in its original language.

Printed source discrepancies retained. Question 1.c explicitly prints $\alpha^2=0$ . In experiment 2 the question's 1.d refers to 1.a, and 1.f refers to itself for the slope; the answer forms instead refer to 1.c and 1.e. Key 1.g for experiment 1 prints $J_k\ddot\alpha+\Omega^2\alpha=0$ after its earlier torque equation. Its radius calculation prints $a=0.32(0.96\,\mathrm m)$ followed by $a=3.1\times 10^{-2}\,\mathrm m$ ; the product and printed result disagree. The regression graph's ordinate prints $2\pi/T^2$ , while the adjacent formula and table use $4\pi^2/T^2$ . The sample table's last row contains 6.97s among times near 5.9s and a printed mean 6.13s; none of these values is recalculated. Experiment 2 key 1.a prints “070p” in its total column. The original answer-sheet page 14 lacks its right outer vertical border, but the complete plotting grid is retained. The ideal-water inertia assumption in the theoretical key and the nonideal-water error explanation in 3.e are both preserved.

Условие

This experimental problem propose an analysis for an electrical black box, which has three terminals - denoted by 1,2,3. To discover the elements that compose it, is provided a measuring device comprising a voltage source variable (denoted by $S$ ), connected in series with an ammeter (denoted by $A$ ); the two terminals of the device are denoted by $P$ and $Q$ . To the same terminals $P$ and $Q$ is mounted a voltmeter (denoted by $V$ ). Ammeter and power supply have negligible internal resistance; internal resistance of the voltmeter can be considered as being infinite.

Whole native measuring circuit, voltmeter/ammeter/variable source/arrows/P/Q and entire three-terminal black-box panel with both original captions.

The terminals 1,2 and $P$ are placed in electrical contact. If terminals 3 and $Q$ are also in electrical contact and the tension furnished by the source varies, pairs of values (indicated by the measuring instruments) are obtained. These data are given in the table 1. Current intensity is positive when the current passes through the ammeter from $P$ to $Q$ .

Table 1

$U$ (V)	−6	−4	−2	0	2	4
$I$ (A)	−0.2	1.2	2.6	4.0	5.4	6.8

Then, terminals 2,3, $P$ are putted in electrical contact. If and terminals 1, $Q$ are also in electrical contact, the pairs of values indicated by the measuring instruments - where the voltage supplied by the source varies - are given in table 2.

Table 2

$U$ (V)	0	2	4	6	8	10
$I$ (A)	−5.2	−4.0	−2.8	−1.6	−0.4	+0.8

Finally, terminals 3,1, $P$ are putted in electrical contact. If and terminals 2, $Q$ are also in electrical contact, the pairs of values indicated by the measuring instruments - where the voltage supplied by the source varies - are given in table 3.

Table 3

$U$ (V)	−6	−4	−2	0	2
$I$ (A)	−0.6	0	0.6	1.2	1.8

Assume that all current-voltage dependencies are linear.

In this problem, calculation of errors is NOT requested.

Task 1 (3 т.)

1.a Plot current - voltage dependence for the data set in Table 1. [0,7 т.]

1.b Determine the numerical values of the intersections with coordinate axes of the graph. Determine also the slope of graph outlined in task 1.a. If applicable, write the result as a fraction. [0,3 т.]

1.c Plot current - voltage dependence for the data set in Table 2. [0,7 т.]

1.d Determine the numerical values of the intersections with coordinate axes of the graph. Determine also the slope of graph outlined in task 1.a. If applicable, write the result as a fraction. [0,3 т.]

1.e Plot current - voltage dependence for the data set in Table 3. [0,7 т.]

1.f Determine the numerical values of the intersections with coordinate axes of the graph outlined in task 1.e. Determine also the slope of graph outlined in task 1.f. If applicable, write the result as a fraction. [0,3 т.]

Task 2 (5 т.)

2.a Determine the values of the electrical resistance of the resistors and electromotive force (emf) of ideal voltage sources that form the simplest circuit (a circuit triangle, delta, $\Delta$ ), which has the behavior described by the above data. Keep in mind that the ideal voltage source connected in series with the resistor having the lowest electrical resistance, has an emf of 10V. [4,6 т.]

2.b Draw the equivalent circuit diagram for black box. Write on diagram the values of electrical resistance and emf of the sources - as they results in the task 2.a. [0,4 т.]

Task 3 (2 т.)

3.a For the equivalent circuit that you have determined in the task no.2, plot the current-voltage dependence, when the terminals $P$ and $Q$ are in electrical contact with terminals 1 and 2 respectively. Write numerical values of the intersections with the axes of coordinates of the graph plotted. [2 т.]

Answer sheet

The complete original unfilled Answer sheet occupies pages 19–26. Pages 19,20,21 contain the three blank current–tension grids and intercept/slope boxes for 1.a–1.f. The form 1.d correctly refers to 1.c and 1.f correctly refers to 1.e, whereas the question's printed references differ. Pages 22–24 retain all three native working pages for 2.a, including both “further calculations” continuations. Page 25 contains 2.b and the start of 3.a; page 26 is the final 3.a blank grid. Points are 1.a 0.70/1.b 0.30/1.c 0.70/1.d 0.30/1.e 0.70/1.f 0.30;2.a 4.60/2.b 0.40;3.a 2.00. The corresponding additional English original repeats these complete forms.

Complete unfilled original answer-sheet physical page 20, all task requests/marks/blank response areas/outer borders/native grid where printed; no sample-key data. — Answer Sheet — original page 20 of 26

Complete unfilled original answer-sheet physical page 21, all task requests/marks/blank response areas/outer borders/native grid where printed; no sample-key data. — Answer Sheet — original page 21 of 26

Complete unfilled original answer-sheet physical page 22, all task requests/marks/blank response areas/outer borders/native grid where printed; no sample-key data. — Answer Sheet — original page 22 of 26

Complete unfilled original answer-sheet physical page 23, all task requests/marks/blank response areas/outer borders/native grid where printed; no sample-key data. — Answer Sheet — original page 23 of 26

Complete unfilled original answer-sheet physical page 24, all task requests/marks/blank response areas/outer borders/native grid where printed; no sample-key data. — Answer Sheet — original page 24 of 26

Complete unfilled original answer-sheet physical page 25, all task requests/marks/blank response areas/outer borders/native grid where printed; no sample-key data. — Answer Sheet — original page 25 of 26

Complete unfilled original answer-sheet physical page 26, all task requests/marks/blank response areas/outer borders/native grid where printed; no sample-key data. — Answer Sheet — original page 26 of 26

Topic was proposed by

Решение

Barem de evaluare şi de notare

Se punctează oricare altă modalitate de rezolvare corectă a problemei.

Problema experimentală nr. 2 – Cutie neagră electrică

1.a

Sarcina de lucru nr. 1

Pentru trasarea caracteristicii curent-tensiune, corespunzătoare datelor din tabelul 1:

Complete native first current-voltage graph, full axes/units/ticks/point line/intercepts.

0,70p. Observaţii:

se acordă câte 0,10p pentru indicarea mărimii şi a unităţii de măsură corespunzătoare fiecăreia dintre axele de coordonate;
se acordă 0,50p pentru marcarea corectă pe grafic a punctelor corespunzătoare setului de date experimentale din tabelul 1.

Punctaj item: 070p (aşa cum este tipărit în coloana totală a originalului).

1.b

Pentru determinarea valorilor pentru intersecţia cu axele de coordonate a caracteristicii curent-tensiune şi pentru panta graficului, corespunzător datelor din tabelul 1:

(0,I_{\mathrm{sc},12})≡(0,4),\quad(U_{\mathrm{cd},12},0)≡\left(-\frac{40}{7},0\right),\quad m_{12}=0.7\,\Omega^{-1}.

0,30p; punctaj item: 0,30p.

1.c

Pentru trasarea caracteristicii curent-tensiune, corespunzătoare datelor din tabelul 2:

Complete native second current-voltage graph, full axes/units/ticks/point line/intercepts.

0,70p. Observaţii:

se acordă câte 0,10p pentru indicarea mărimii şi a unităţii de măsură corespunzătoare fiecăreia dintre axele de coordonate;
se acordă 0,50p pentru marcarea corectă pe grafic a punctelor corespunzătoare setului de date experimentale din tabelul 2.

Punctaj item: 0,70p.

1.d

Pentru determinarea valorilor pentru intersecţia cu axele de coordonate a caracteristicii curent-tensiune şi pentru panta graficului, corespunzător datelor din tabelul 2:

(0,I_{\mathrm{sc},23})≡(0,-5.2),\quad(U_{\mathrm{cd},23},0)≡\left(\frac{26}{3},0\right),\quad m_{23}=\frac{12}{20}\,\Omega^{-1}.

0,30p; punctaj item: 0,30p.

1.e

Pentru trasarea caracteristicii curent-tensiune, corespunzătoare datelor din tabelul 3:

Complete native third current-voltage graph, full axes/units/ticks/point line/intercepts.

0,70p. Observaţii:

se acordă câte 0,10p pentru indicarea mărimii şi a unităţii de măsură corespunzătoare fiecăreia dintre axele de coordonate;
se acordă 0,50p pentru marcarea corectă pe grafic a punctelor corespunzătoare setului de date experimentale din tabelul 3.

Punctaj item: 0,70p.

1.f

Pentru determinarea valorilor pentru intersecţia cu axele de coordonate a caracteristicii curent-tensiune şi pentru panta graficului, corespunzător datelor din tabelul 3:

(0,I_{\mathrm{sc},31})≡(0,1.2),\quad(U_{\mathrm{cd},31},0)≡(-4,0),\quad m_{31}=0.3\,\Omega^{-1}.

0,30p; punctaj item: 0,30p.

2.a

Sarcina de lucru nr. 2

Pentru schema unui circuit triunghi echivalent cu cutia neagră:

Entire original equivalent triangle with all R12/R23/R31 and E12/E23/E31 polarity arrows and terminals.

0,40p.

Schema echivalentă a circuitului, pentru primul set de măsurări, în cursul cărora sunt legate împreună bornele 1,2,P şi respectiv 3,Q:

Complete original first-measurement circuit, both i prime/i double prime arrows, all wires/terminals/source/meters/branches.

0,40p.

Expresia caracteristicii curent-tensiune a cutiei negre, pentru legarea $(1,2,P),(3,Q)$ :

i=U\left(\frac 1{R_{23}}+\frac 1{R_{31}}\right)+\left(-\frac{E_{23}}{R_{23}}+\frac{E_{31}}{R_{31}}\right).

Expresia pantei $m_{12}=\dfrac 1{R_{23}}+\dfrac 1{R_{31}}$ ; expresia intercepţiei $n_{12}=-\dfrac{E_{23}}{R_{23}}+\dfrac{E_{31}}{R_{31}}$ —0,40p.

Expresiile pentru intersecţiile cu axele de coordonate:

I_{\mathrm{sc},12}=-\frac{E_{23}}{R_{23}}+\frac{E_{31}}{R_{31}},\quad U_{\mathrm{cd},12}=\frac{\dfrac{E_{23}}{R_{23}}-\dfrac{E_{31}}{R_{31}}}{\dfrac 1{R_{23}}+\dfrac 1{R_{31}}}.

0,40p.

Expresia caracteristicii curent-tensiune a cutiei negre, pentru legarea $(2,3,P),(1,Q)$ :

i=U\left(\frac 1{R_{31}}+\frac 1{R_{12}}\right)+\left(-\frac{E_{31}}{R_{31}}+\frac{E_{12}}{R_{12}}\right).

Expresia pantei $m_{23}=\dfrac 1{R_{31}}+\dfrac 1{R_{12}}$ ; expresia intercepţiei $n_{23}=-\dfrac{E_{31}}{R_{31}}+\dfrac{E_{12}}{R_{12}}$ —0,40p.

Expresiile pentru intersecţiile cu axele de coordonate:

I_{\mathrm{sc},23}=-\frac{E_{31}}{R_{31}}+\frac{E_{12}}{R_{12}},\quad U_{\mathrm{cd},23}=\frac{\dfrac{E_{31}}{R_{31}}-\dfrac{E_{12}}{R_{12}}}{\dfrac 1{R_{31}}+\dfrac 1{R_{12}}}.

0,40p.

Expresia caracteristicii curent-tensiune a cutiei negre, pentru legarea $(3,1,P),(2,Q)$ :

i=U\left(\frac 1{R_{12}}+\frac 1{R_{23}}\right)+\left(-\frac{E_{12}}{R_{12}}+\frac{E_{23}}{R_{23}}\right).

Expresia pantei $m_{31}=\dfrac 1{R_{12}}+\dfrac 1{R_{23}}$ ; expresia intercepţiei $n_{31}=-\dfrac{E_{12}}{R_{12}}+\dfrac{E_{23}}{R_{23}}$ —0,40p.

Expresiile pentru intersecţiile cu axele de coordonate:

I_{\mathrm{sc},31}=-\frac{E_{12}}{R_{12}}+\frac{E_{23}}{R_{23}},\quad U_{\mathrm{cd},31}=\frac{\dfrac{E_{12}}{R_{12}}-\dfrac{E_{23}}{R_{23}}}{\dfrac 1{R_{12}}+\dfrac 1{R_{23}}}.

0,40p.

Determinarea valorilor rezistenţelor electrice şi ale tensiunilor electromotoare ale surselor, care formează circuitul electric:

R_{12}=10\,\Omega,\quad R_{23}=5\,\Omega,\quad R_{31}=2\,\Omega,\quad E_{31}=10\,\mathrm V,\quad E_{23}=5\,\mathrm V,\quad E_{12}=-2\,\mathrm V.

1,40p. Punctaj item: 4,60p.

2.b

Pentru desenarea schemei circuitului electric echivalent, cu indicarea valorilor elementelor constitutive:

Complete numerical triangle circuit with all10ohm/5ohm/2ohm and2V/5V/10V values/polarity arrows and1/2/3terminals.

0,40p; punctaj item: 0,40p.

3.a

Sarcina de lucru nr. 3

Pentru schema echivalentă a circuitului realizat prin legarea $(1,P)$ şi $(2,Q)$ :

Complete original P-to1/Q-to2 equivalent branches with all resistor/source values, current arrows/meters/variable source/wires.

Determinarea dependenţei curent–tensiune pentru circuitul specificat:

i=\frac{17}{70}U+\frac{164}{70}.

1,00p.

Trasarea graficului pentru dependenţa curent-tensiune, în cazul în care terminalele $P$ şi $Q$ se leagă respectiv la terminalele 1 şi 2:

Complete original final P-to1/Q-to2 current-voltage graph and both full axes/labels/units/ticks/intercepts.

0,60p.

Valoarea intensităţii curentului electric de scurtcircuit $i_{\mathrm{sc}}=\dfrac{164}{70}\,\mathrm A$ ; valoarea tensiunii de circuit deschis $U_{\mathrm{cd}}=-\dfrac{164}{17}\,\mathrm V$ —0,40p. Punctaj item: 2,00p.

Punctaj total — Problema experimentală nr. 2

10p

Оригинал в Архива: exp_problems.pdf · официални решения: rmph_experiment_sol.pdf · допълнителни данни: rmph_experiment_sub.pdf