cee291_10_sp_hw9_sol

# cee291_10_sp_hw9_sol - Spring 2010 Homework 9 CEE 291...

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Spring 2010 Homework 9 – CEE 291 Problem 1 A platinum RTD (α=0.00392 0 C -1 ) is to be calibrated. The probe is used in the Wheatstone bridge circuit in the sketch. The bridge resistances have accuracies of ± 0.001 Ω. At 0 0 C, the bridge balances with R 1 = 100 Ω, and at 100 0 C the bridge balances with R 1 = 139.2 Ω. R 2 = R 3 = 100 Ω. a) For the bridge operated in a balanced mode, determine the RTD resistance at 0 0 C and 100 0 C, and the uncertainty in each value. : = = = * = For a balanced bridge RRTDR1 R3R2 RRTD R1R3R2 100Ω 100Ω100Ω 100Ω =∂ ∂ +∂ ∂ +∂ ∂ uRTD R R1uR12 R R2uR22 R R3uR32 = = . = where ud uncertainty in the resistances 0 001Ω uR1 = = uR2 uR3 , = . =± . uRTD 0 0 0013 0 001732Ω , = . + . =± . uRTD 100 0 0011 21 3922 0 00221Ω b) For the bridge operated in a balanced mode, determine the temperature uncertainty for a measured temperature that results in R 1 = 115 Ω. Assume the uncertainty in α = ± 0.00001. =∂ ∂ +∂ ∂ , ∂ ∂ = ∂ ∂ =- - uT T R uRTD2 T α uα2 T R 1αR0 and T α R R0α2R0 = . + = . , ∂ ∂ = . = . , ∂ ∂ =- uRTD 0 0011 21152 0 00191Ω T R 10 392 2 55102 T α . =- . 150 003922100 9761 558 = . uα 0 00001 = . . +- . * . =± . uT 10 392 0 001912 9761 558 0 000012 0 0977Ω c) If the bridge is operated in an unbalanced mode from the balance condition at 0 0 C, determine and plot bridge output voltage, Eo, versus temperature. The bridge input voltage, Ei, is 10 V. = [ + . - ]

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cee291_10_sp_hw9_sol - Spring 2010 Homework 9 CEE 291...

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