Lab 4 Temperature Coefficient of Resistance PDF

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Lab experiment with calculations and data on Temperature coefficient of resistance....

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Temperature Coefficient of Resistance Austin Glass (Lab Partners: Lizzy Ainsworth, Joseph Gunn, Anmol Jarang) 9/29/17 ABSTRACT For metals used as electrical conductors, there is a relationship between resistance and temperature. This relationship depends upon what is called the temperature coefficient of resistance. This experiment was performed by measuring temperature, resistance, and length in order to calculate slopes. Error analysis was performed in order to verify the theoretical values. The error ranges were (0.00333/°C ≤0.00396/°C ≤0.00533/°C) for the conductor which supported the theoretical value, and (3250K≤3410K≤3454K) for the semiconductor which failed to support the theoretical value. THEORY Metals used as electrical conductors typically have a relationship between resistance and temperature. This relationship can be demonstrated mathematically by the equation

which can be rewritten as

Here, α is the temperature coefficient of resistance. Rt is the value of resistance of the metal conductor at a temperature (°C), and Ro is the value of resistance of the metallic conductor at 0°C. Most metals have a small, positive temperature coefficient of resistance and thus a linear plot. In contrast thermistors have large, negative values; however, the plots for these are typically non-linear and given by the equation

where R is the resistance in ohms at a temperature t (in Kelvin), Ra is the resistance at the lowest temperature used, and β is a property of the material (K). The equation can be rewritten as where x= 1/t -1/ta OBJECTIVE The purpose of this experiment is to determine the temperature coefficients of resistance for both thermistors and a metal (copper wire).

PROCEDURE A vessel from the apparatus was filled with water and a thermometer was put through the hole in the bakelite cover. A connecting cord was attached to the heating unit prongs and to the 115 volt A.C. power supply. The temperature sensor was connected and the datastudio program ran. The binding posts on the unit were connected to the Wheatstone bridge terminals (Figure 1), and the resistance was measured. Ice was used to measure the resistance below room temperature. Measurements were taken to a tenth of an ohm and a tenth of a degree. The temperature was increased by 5 degrees (water was stirred continuously). The heater was turned off two degrees before the desired temperature. When the temperature had reached a maximum, temperature and resistance measurements were recorded. The process was repeated using steps of 5 degrees until a temperature of 70°C was reached (a minimum of 6 steps was required).

Figure 1. Setup of Wheatstone Bridge DATA Table 1. Measurements for a Semiconductor Temperature ( C ) Rk (Ω) L1 (cm) L2 (cm) 23.3 30 44.30 55.70 28.3 30 42.70 57.30 33.3 30 37.30 62.70 38.3 30 33.60 66.40 43.3 30 29.40 70.60 48.3 30 26.10 73.90 53.3 30 23.00 77.00 58.3 30 20.30 79.70 63.3 30 17.40 82.60 68.3 30 15.60 84.40 73.3 30 13.60 86.40

Table 2. Measurements for a Conductor Temperature ( C ) Rk (Ω) L1 (cm) L2 (cm) 25.3 1 50.0 50.0 30.3 1 51.3 48.7 35.3 1 51.6 48.4 40.3 1 52.2 47.8 45.3 1 52.6 47.4 50.3 1 52.9 47.1 55.3 1 53.3 46.7 60.3 1 53.4 46.6 65.3 1 53.8 46.2 70.3 1 54.2 45.8 75.3 1 54.8 45.2

T(K)=T(C)+273.15

CALCULATIONS 23.3C+273.15=296K

Ru=Rk(L1/L2)

30.00Ω(44.30cm/55.70cm)=23.86Ω

1/T=1/T(K)

1/296K=0.00337K-1

ln(R)=ln(Ru)

ln(23.86Ω)=3.17

α=slope/intercept

0.00370(Ω/°C) / 0.933Ω =0.00396/°C

QUALITATIVE ERROR ANALYSIS One cause for potential error within the experiment may have stemmed from the heating system. The recording of lengths was slightly off from the particular temperature point that was recorded since the temperature increased at a faster rate than the length was able to be determined. Another possible cause for error could have occurred due to the close proximity of the thermometer to the heat source. The water was stirred; however, the reading may not have been accurate due to the intensity of the heat coming from the source. QUANTITATIVE ERROR ANALYSIS In this experiment, two graphs were formed in order to obtain slope values. Linear charts were made, and excel trend lines were used to obtain the slopes. For the case of a conductor, the slope over the intercept was calculated to form an α value. The α value in the case of the conductor was 0.00396/°C. The calculated values from the experiments were compared to theoretical values. The error range for the case of a conductor was (0.00333/°C ≤0.00396/°C ≤0.00533/°C). The error range for the case of the semiconductor was (3250K≤3410K≤3454K).

RESULTS

Figure 2. ln(R) v. 1/T for a Semiconductor 3.50000 3.00000

ln(R)

2.50000

f(x) = 3454.6 x − 8.4 R² = 1

2.00000 1.50000 1.00000 0.50000 0.00000 0.00280 0.00290 0.00300 0.00310 0.00320 0.00330 0.00340 0.00350

1/T ( C )

Figure 3. R v. T for a Conductor 1.400000

Resistance (ohms)

1.200000 1.000000

f(x) = 0 x + 0.93 R² = 0.97

0.800000 0.600000 0.400000 0.200000 0.000000 20

30

40

50

60

T( C )

Table 3. Calculations for a Semiconductor Temperature (K) Ru (Ω) 1/T (K-1) ln(Ru) 296.45 23.86 0.00337 3.17220 301.45 22.36 0.00332 3.10710 306.45 17.85 0.00326 2.88183 311.45 15.18 0.00321 2.72003 316.45 12.49 0.00316 2.52516 321.45 10.60 0.00311 2.36042 326.45 8.96 0.00306 2.19289 331.45 7.64 0.00302 2.03355 336.45 6.32 0.00297 1.84366 341.45 5.55 0.00293 1.71290

70

80

346.45

4.72

0.00289

1.55228

Table 4. Calculations for a Conductor Ru (Ω 1.000000 1.053388 1.066116 1.092050 1.109705 1.123142 1.141328 1.145923 1.164502 1.183406 1.212389 Error range Conductor:0.00333/°C ≤0.00396/°C ≤0.00533/°C Error range Semiconductor:3250K≤3410K≤3454K CONCLUSION For the case of the conductor, the error range in the α value was (0.00333/°C ≤0.00396/°C ≤0.00533/°C). Since the calculated value of 0.00396/°C fell within the theoretical range, the experiment supported the temperature coefficient of resistance for the case. For the case of the semiconductor, the error range was (3250K≤3410K≤3454K). Since the slope of 3454K did not fall within the theoretical range, the experiment failed to support the temperature coefficient of resistance for the case. It is important to note, however, that the experimental temperature coefficient of resistance for the semiconductor was just over falling within the theoretical range....