mws_ele_inp_txt_direct_examples

mws_ele_inp_txt_direct_examples - Chapter 05.02 Direct...

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05.02.1 Chapter 05.02 Direct Method of Interpolation – More Examples Electrical Engineering Example 1 Thermistors are used to measure the temperature of bodies. Thermistors are based on materials’ change in resistance with temperature. To measure temperature, manufacturers provide you with a temperature vs. resistance calibration curve. If you measure resistance, you can find the temperature. A manufacturer of thermistors makes several observations with a thermistor, which are given in Table 1. Table 1 Temperature as a function of resistance. R   ohm T   C 1101.0 911.3 636.0 451.1 25.113 30.131 40.120 50.128 Figure 1 Resistance vs. temperature.
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05.02.2 Chapter 05.02 Determine the temperature corresponding to 754.8 ohms using the direct method of interpolation and a first order polynomial. Solution For first order polynomial interpolation (also called linear interpolation), we choose the temperature given by  R a a R T 1 0 Figure 2 Linear interpolation. Since we want to find the temperature at 8 . 754 R , and we are using a first order polynomial, we need to choose the two data points that are closest to 8 . 754 R that also bracket 8 . 754 R to evaluate it. The two points are 3 . 911 0 R and 0 . 636 1 R . Then  131 . 30 , 3 . 911 0 0 R T R  120 . 40 , 0 . 636 1 1 R T R gives   131 . 30 3 . 911 3 . 911 1 0 a a T   120 . 40 0 . 636 0 . 636 1 0 a a T Writing the equations in matrix form, we have 120 . 40 131 . 30 0 . 636 1 3 . 911 1 1 0 a a Solving the above two equations gives 197 . 63 0 a 036284 . 0 1 a Hence  R a a R T 1 0  0 0 , y x   1 1 , y x   x f 1 x y
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Direct Method of Interpolation – More Examples: Electrical Engineering 05.02.3 3 . 911 0 . 636 , 036284 . 0 197 . 63 R R At 8 . 754 R ,    8 . 754 036284 . 0 197 . 63 8 . 754 T C 809 . 35 Example 2 Thermistors are used to measure the temperature of bodies. Thermistors are based on materials’ change in resistance with temperature. To measure temperature, manufacturers provide you with a temperature vs. resistance calibration curve. If you measure resistance, you can find the temperature. A manufacturer of thermistors makes several observations with a thermistor, which are given in Table 2. Table 2
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This note was uploaded on 06/12/2011 for the course EML 3041 taught by Professor Kaw,a during the Spring '08 term at University of South Florida - Tampa.

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mws_ele_inp_txt_direct_examples - Chapter 05.02 Direct...

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