Relazione Misura del coefficiente di temperatura della resistenza di vari materiali

ENTO °C

Temperature 28,0 65,6 964,0

R1 Ω R2 Ω

°C 28,5 / /

18,0 60,4 1336,0 29,0 65,8 960,0

18,5 / / 29,5 / /

19,0 / / 30,0 66,4 940,0

19,5 61,0 1278,0 30,5 66,8 920,0

20,0 61,8 1210,0 31,0 / /

20,5 / / 31,5 68,2 886,0

21,0 62,0 1190,0 32,0 / /

21,5 62,2 1166,0 32,5 68,6 874,0

22,0 62,4 1154,0 33,0 69,2 858,0

22,5 62,6 1140,0 33,5 70,8 818,0

23,0 62,8 1112,0 34,0 71,4 810,0

23,5 / / 34,5 72,0 794,0

24,0 63,2 1100,0 35,0 72,4 788,0

24,5 / / 35,5 73,0 774,0

25,0 63,4 1064,0 36,0 75,0 738,0

25,5 63,8 1064,0 36,5 / /

26,0 63,8 1056,0 37,0 76,0 728,0

26,5 64,0 1034,0 37,5 76,6 720,0

27,0 64,8 1010,0 38,0 77,0 710,0

27,5 65,2 992,0

[]

1 La sensibilità di misura di tale strumento varia al variare della grandezza presa. Nella Tabella

[1] e nella Tabella [2] si possono notare chiaramente i passaggi da un multiplo all’altro della

misura di resistenza con la conseguente modificazione del valore minimo rilevato dallo

strumento. Temperatur

Temperatur R1 Ω R2 Ω

R1 Ω R2 Ω e °C

e °C 61,5 206,2 346,0

39,0 79,4 690,0 62,0 211,0 342,0

39,5 / / 62,5 215,0 340,0

40,0 80,4 672,0 63,0 220,0 338,0

40,5 / / 63,5 229,4 334,0

41,0 81,6 654,0 64,0 231,0 330,0

41,5 83,2 642,0 64,5 266,8 312,0

42,0 86,6 612,0 65,0 277,0 310,0

42,5 88,0 602,0 65,5 281,0 308,0

43,0 90,0 590,0 66,0 286,0 306,0

43,5 90,6 584,0 66,5 / /

44,0 91,6 572,0 67,0 304,0 300,0

44,5 94,0 562,0 67,5 317,2 296,0

45,0 95,6 552,0 68,0 374,8 284,0

45,5 96,4 548,0 68,5 380,0 282,0

46,0 98,2 540,0 69,0 456,0 270,0

46,5 99,0 534,0 69,5 / /

47,0 / / 70,0 / /

47,5 102,8 520,0 70,5 532,0 264,0

48,0 107,0 502,0 71,0 / /

48,5 110,6 492,0 71,5 570,0 260,0

49,0 / / 72,0 730,0 248,0

49,5 112,0 586,0 72,5 800,0 240,0

50,0 114,0 580,0 73,0 880,0 236,0

50,5 122,0 454,0 73,5 / /

51,0 / / 74,0 1118,0 222,0

51,5 125,0 450,0 74,5 1190,0 218,0

52,0 127,0 444,0 75,0 1332,0 218,0

52,5 / / 75,5 1480,0 216,0

53,0 130,0 440,0 76,0 1572,0 212,0

53,5 142,0 416,0 76,5 / /

54,0 144,0 412,0 77,0 1890,0 208,0

54,5 148,0 408,0 77,5 2040,0 206,0

55,0 154,6 400,0 78,0 2380,0 204,0

55,5 155,0 396,0 78,5 2540,0 200,0

56,0 160,0 386,0 79,0 3100,0 196,0

56,5 161,8 384,0 79,5 / /

57,0 164,0 384,0 80,0 3240,0 194,0

57,5 168,2 374,0 80,5 / /

58,0 173,0 370,0 81,0 3920,0 186,0

58,5 183,0 364,0 81,5 4900,0 182,0

59,0 188,6 362,0 82,0 / /

59,5 190,4 360,0 82,5 5300,0 180,0

60,0 193,0 356,0

60,5 197,0 354,0

61,0 205,8 348,0 83,0 5840,0 178,0

83,5 7000,0 176,0

Temperature R1 Ω R2 Ω

°C 7380,0 172,0

84,0

84,5 8200,0 170,0

85,0 8660,0 168,0

85,5 9900,0 166,0

86,0 10900,0 164,0 Simbolo di NTC

86,5 11400,0 162,0

87,0 15000,0 158,0

87,5 16000,0 156,0

88,0 19000,0 152,0

88,5 21500,0 150,0

89,0 24600,0 146,0

89,5 26300,0 146,0

90,0 29500,0 142,0

90,5 / /

91,0 32600,0 140,0 Simbolo di PTC

91,5 42900,0 136,0 Temperature °C R1 Ω R2 Ω

RAFFREDDAMEN Tabella 2460,0 199,0

79,0

TO [2] 2200,0 202,0

78,5

Temperature °C R1 Ω R2 Ω 2118,0 204,6

78,0

/ /

91,5 1850,0 208,4

77,5

/ /

91,0 1830,0 209,0

77,0

32000,0 139,0

90,5 1404,0 215,6

76,5

22000,0 146,0

90,0 1336,0 217,8

76,0

21400,0 146,8

89,5 1334,0 218,2

75,5

21360,0 147,4

89,0 1334,0 219,0

75,0

21360,0 146,4

88,5 1222,0 221,0

74,5

20520,0 146,6

88,0 / /

74,0

19160,0 149,6

87,5 / /

73,5

18000,0 150,0

87,0 1200,0 222,0

73,0

16820,0 151,6

86,5 994,0 229,8

72,5

16360,0 152,4

86,0 950,0 231,0

72,0

15980,0 153,0

85,5 928,0 231,4

71,5

14300,0 154,6

85,0 928,0 232,0

71,0

13320,0 155,6

84,5 814,0 237,0

70,5

10000,0 162,0

84,0 718,0 239,2

70,0

8800,0 164,6

83,5 676,0 243,0

69,5

8780,0 164,8

83,0 596,0 250,6

69,0

7300,0 169,2

82,5 454,0 264,4

68,5

7100,0 170,0

82,0 394,0 270,0

68,0

6800,0 171,0

81,5 394,0 273,8

67,5

6680,0 172,0

81,0 364,0 272,4

67,0

3080,0 194,6

80,5 324,0 283,0

66,5

2640,0 197,4

80,0 2620,0 198,8

79,5

Temperature °C R1 Ω R2 Ω Temperature °C R1 Ω R2 Ω

302,0 290,0

66,0 165,4 366,6

53,0

296,8 291,0

65,5 160,8 370,2

52,5

226,2 304,8

65,0 160,6 373,2

52,0

/ /

64,5 160,2 373,6

51,5

266,6 307,2

64,0 159,4 374,0

51,0

258,8 307,6

63,5 159,0 374,2

50,5

249,8 310,0

63,0 158,4 374,4

50,0

237,2 316,6

62,5 156,6 376,2

49,5

230,0 317,4

62,0 154,8 377,8

49,0

214,8 325,8

61,5 155,0 377,0

48,5

/ /

61,0 153,6 377,4

48,0

/ /

60,5 / /

47,5

220,2 323,0

60,0 154,2 377,8

47,0

220,2 323,8

59,5 154,4 378,0

46,5

/ /

59,0 / /

46,0

212,8 328,6

58,5 130,0 422,0

45,5

213,0 328,8

58,0 129,6 422,0

45,0

199,8 336,6

57,5 129,2 422,0

44,5

198,6 338,4

57,0 129,0 424,0

44,0

197,8 343,8

56,5 128,0 424,0

43,5

190,0 344,2

56,0 / /

43,0

187,2 347,0

55,5 126,6 426,0

42,5

182,0 350,8

55,0 126,6 426,0

42,0

180,6 351,8

54,5 125,4 428,0

41,5

179,8 353,2

54,0 124,6 428,0

41,0

166,6 364,6

53,5 124,4 430,0

40,5 123,2 432,0

40,0

I diversi colori corrispondo alle differenti sensibilità di misura del tester digitale che, in mancanza

di misure reiterate, corrispondono agli errori totali da associare a ciascuna misura; la legenda è la

seguente. Colore Sensibilità strumento

Rosso ±0.2Ω

Verde ±2 Ω

Blu ±20 Ω

4. Grafici

I presenti sono i grafici di tendenza delle due resistenze in base alla temperatura; il primo riguarda

Tabella [1]

50000.0

45000.0

40000.0

35000.0

30000.0

25000.0

20000.0

15000.0

10000.0

5000.0

0.0

18 21 24 27 30 33 36 39 42 45 48 51 54 57 60 63 66 69 72 75 78 81 84 87 90 70

la fase di riscaldamento, il secondo quella di raffreddamento.

R 1

Tabella [2]

35000.0

30000.0

25000.0

20000.0

15000.0

10000.0

5000.0

0.0

.5 .0 .5 .0 .5 .0 .5 .0 .5 .0 .5 .0 .5 .0 .5 .0 .5 .0 .5 .0 .5 .0 .5 .0 .5 .0 .5

91 89 86 84 81 79 76 74 71 69 66 64 61 59 56 54 51 49 46 44 41 39 36 34 31 29 26 R

R 2

1

raffreddamento 91,5 91

5. Medie ed errori

Essendo in possesso di dati sia nella fase di riscaldamento dell’acqua che in quella di

raffreddamento è stato necessario calcolare la media tra le misure, pesata in caso di sensibilità di

misura diverse. Temperature

M R1 Ω R2 Ω

°C

T 37,0 76,0 728,0

1 37,5 76,6 720,0

1 38,0 77,0 710,0

1 38,5 / /

1 39,0 79,4 690,0

2 39,5 / /

2 40,0 101,8 552,0

2

Temperature R1 Ω R2 Ω 40,5 124,4 430,0

2 °C

Temperature 41,0 103,1 541,0

2 R1 Ω R2 Ω

56,5 175,9 344,2

°C 41,5 104,3 535,0

2 57,0 180,9 338,9

74,5 1206,0 221,0 42,0 106,6 519,0

2 57,5 183,4 337,0

75,0 1333,0 216,8 42,5 107,3 514,0

2 58,0 186,4 329,2

75,5 1351,0 218,2 43,0 90,0 590,0

2 58,5 198,0 329,0

76,0 1453,0 217,7 43,5 109,3 504,0

2 59,0 200,7 362,0

76,5 1404,0 213,5 44,0 110,3 498,0

2 59,5 205,3 324,2

77,0 1613,0 209,0 44,5 111,6 492,0

2 60,0 206,6 323,3

77,5 1410,3 208,4 45,0 112,6 487,0

2 60,5 208,6 354,0

78,0 1835,4 204,6 45,5 113,2 485,0

2 61,0 205,8 348,0

78,5 1856,8 202,0 46,0 98,2 540,0

2 61,5 210,5 326,0

79,0 2127,7 199,0 46,5 126,7 456,0

2 62,0 212,9 317,6

79,5 2620,0 196,8 47,0 154,2 374,1

2 62,5 222,5 316,8

80,0 2850,0 197,4 47,5 102,8 520,0

2 63,0 228,6 310,3

80,5 1310,0 192,7 48,0 130,3 378,6

2 63,5 239,6 307,9

81,0 3280,0 172,1 48,5 132,8 378,1

2 64,0 244,9 307,4

81,5 3990,0 171,1 49,0 154,8 374,1

3 64,5 266,7 312,0

82,0 3340,0 168,3 49,5 134,3 378,3

3 65,0 251,6 304,9

82,5 6050,0 169,3 50,0 136,2 376,4

3 65,5 253,6 291,2

83,0 6470,0 164,9 50,5 140,5 375,0

3 66,0 291,4 290,2

83,5 7150,0 164,7 51,0 159,4 370,3

3 66,5 148,4 280,2

84,0 8080,0 162,1 51,5 142,6 374,4

3 67,0 304,0 272,7

84,5 8500,0 155,7 52,0 143,8 373,9

3 67,5 317,3 274,0

85,0 9330,0 154,7 52,5 160,8 366,5

3 68,0 374,7 270,1

85,5 11610,0 153,1 53,0 145,4 367,3

3 68,5 387,0 264,6

86,0 12600,0 152,5 53,5 153,7 365,1

3 69,0 425,0 250,8

86,5 13690,0 151,7 54,0 155,3 353,8

3 69,5 676,0 240,6

87,0 15680,0 150,1 54,5 163,9 352,4

3 70,0 718,0 236,8

87,5 16410,0 149,7 55,0 167,6 351,3

3 70,5 604,0 237,3

88,0 18500,0 146,7 55,5 168,5 347,5

3 71,0 928,0 229,7

88,5 20330,0 146,4 56,0 173,6 344,6

71,5 692,0 231,7

89,0 22560,0 147,4

72,0 829,0 231,2

89,5 23830,0 146,8

72,5 864,0 229,9

90,0 25430,0 154,5

73,0 915,0 222,1

90,5 10700,0 151,5

73,5 / /

91,0 27300,0 152,3

74,0 1159,0 222,0

91,5 37450,0 151,4

Ogni valore presente nella Tabella [3] è caratterizzato da un colore come in quelle precedenti.

Questa volta, però, tali colori rappresentano l’errore totale sulle misure. La legenda è la seguente:

Colore Errore

Rosso ±0.2Ω

Verde ±2Ω

Blu ±20Ω

Come già accennato precedentemente, tra le misure con lo stesso errore è stata effettuata una

semplice media; tra quelle in cui esso è diverso è stata applicata la regola della media pesata in

modo da dare maggior importanza a quei valori accompagnati da un errore minore.

La formula utilizzata è la seguente:

δ R

∑ i i

=

R m δ i

δ

Dove rappresenta il “peso” di ogni misura, calcolato come:

i

1

=

δ 2

σ

L’errore da associare alla media si ottiene:

δ i

∑ ¿

¿

¿

=¿

σ́

Tali errori sono risultati coincidenti con quelli del precedente prospetto delle sensibilità di misura

degli strumenti – assimilati poi all’errore totale sulle misure – quindi ho omesso una

differenzazione tra quelli e questo calcolato con le formule appena descritte.

6. Best-fit

Fare un best-fit vuol dire trovare quella retta che meglio approssima dei punti sperimentali.

Supponendo che l’equazione della retta sia del tipo Y = aX, lo scopo del best-fit è di trovare quella

retta (cioè il coefficiente a) per il quale