Mechanical Measurements HW2 Solution

Mechanical Measurements HW2 Solution - PROBLEM 5.9 KNOWN...

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PROBLEM 5.9 KNOWN: Four resistors are available: two rated at R = 500 ± 50 and two rated at R = 2000 ± 5% . FIND: Best design combination to form R T = 1000 SOLUTION We can combine the resistors in series or in parallel. Consider as Case 1, a series arrangement and as Case 2, a parallel arrangement. Case 1 R T = R 1 + R 2 If we use the two 500 resistors, then 1 R d u = ± 50 2 R d u = ± 50 The propagation of uncertainty through to R T is estimated by 1 2 2 2 1/ 2 1 2 ( ) [( ) ( ) ] T R R T T d R d d R R u u u R R = ± + = 1 2 2 2 [(1* ) (1* ) R R d d u u ± + = 71 ± (95%) Case 2 1 2 1 2 T R R R R R = + If we use the two 2000 resistors, then 1 R d u = ± 100 2 R d u = ± 100 The propagation of uncertainty through to R T is estimated by 1 2 2 2 1/ 2 1 2 ( ) [( ) ( ) ] T R R T T d R d d R R u u u R R = ± + = 1 2 2 2 1/ 2 2 1 2 1 1 2 2 2 1 2 1 2 1 2 1 2 [({ }* ) ({ }* ) ] ( ) ( ) R R d d R R R R R R u u R R R R R R R R ± - + - + + + +
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