mws_ele_inp_txt_ndd_examples

mws_ele_inp_txt_ndd_examples - Chapter 05.03 Newtons...

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05.03.1 Chapter 05.03 Newton’s Divided Difference 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
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05.03.2 Chapter 05.03 Figure 1 Resistance vs. temperature. Determine the temperature corresponding to 754.8 ohms using Newton’s divided difference method of interpolation and a first order polynomial. Solution For linear interpolation, the temperature is given by ) ( ) ( 0 1 0 R R b b R T 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 R and 0 . 636 R . Then , 3 . 911 0 R 131 . 30 ) ( 0 R T , 0 . 636 1 R 120 . 40 ) ( 1 R T gives ) ( 0 0 R T b 131 . 30 0 1 0 1 1 ) ( ) ( R R R T R T b 3 . 911 0 . 636 131 . 30 120 . 40 036284 . 0 Hence
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Newton’s Divided Difference Interpolation-More Examples: Electrical Engineering 05.03.3 ) ( ) ( 0 1 0 R R b b R T ), 3 . 911 ( 036284 . 0 131 . 30 R 3 . 911 0 . 636 R At 8 . 754 R ) 3 . 911 8 . 754 ( 036284 . 0 131 . 30 ) 8 . 754 ( T C 809 . 35 If we expand ), 3 . 911 ( 036284 . 0 131 . 30 ) ( R R T 3 . 911 0 . 636 R we get , 036284 . 0 197 . 63 ) ( R R T 3 . 911 0 . 636 R This is the same expression that was obtained with the direct method. 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 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 Determine the temperature corresponding to 754.8 ohms using Newton’s divided difference method of interpolation and a second order polynomial. Find the absolute relative approximate error for the second order polynomial approximation.
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mws_ele_inp_txt_ndd_examples - Chapter 05.03 Newtons...

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