HW-6_solutions

HW-6_solutions - PROBLEM 8.5 KNOWN: A thermistor has a...

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PROBLEM 8.5 KNOWN: A thermistor has a resistance of 20,000 at 100 ° C. β = 3650 ° C R o = 20,000 R = 500 FIND: The temperature corresponding to a thermistor resistance of 500 . SOLUTION: From (8.11) RR e o TT o = β 11 Letting R o = 20,000 3650 373 500 20,000 T Re ⎛⎞ ⎜⎟ ⎝⎠ == and ln500 ln 20,000 3650 373 T =+ Solving for T T = 598.7 K = 325.7 ° C
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PROBLEM 8.6 KNOWN: The uncertainty in temperature 0.005 T uC = ±° . FIND: Required uncertainty in measured resistance. ASSUMPTIONS: Initially assume that we wish to find the required uncertainty in resistance measurement as if it were the only contributor to the total uncertainty. In addition, this problem is open-ended to some extent, in that some nominal value of R o must be assumed, or a range of values for R o examined. SOLUTION: With () [] RR TT oo =+− 1 α and α = 0.003925 ° C -1 , we can express u T R u TR = Then 1 o o R R ⎛⎞ ⎜⎟ ⎝⎠ =+ ∂α T o = 1 Taking R o = 100 ( ) o 1 2.55 C/ 0.003925 100 T R = =Ω and the uncertainty in resistance is u R = ± 000196 .
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HW-6_solutions - PROBLEM 8.5 KNOWN: A thermistor has a...

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