A displacement transducer has the following specifications: Linearity error ± 0.25% reading Drift ± 0.05%/○C reading Sensitivity error ± 0.25% reading Excitation 10 – 25 V dc Output 0 – 5 V dc Range 0 – 5 cm The transducer output is to be indicated on a voltmeter having a stated accuracy of ± 0.1% reading with a resolution of 10 μV. The system is to be used at room temperature, which can vary by ±10○C. Estimate an uncertainty in a nominal displacement of 2 cm at the design stage. Assume 95% confidence. Assume sensitivity is K = 1 V/cm.

The Estimated uncertainty in a nominal displacement of 2 cm at the design stage is plus or minus 0.0124cm

Explanation:

uncertainty in a nominal displacement

= (u^2 + v^2)^(1/2)

assume from specifications that k = 5v/5cm

                                                         = 1v/cm

u^2 = (0.0025*2)^(2) + (0.005*10*2)^2 + (0.0025*2)^2

      = 0.01225v

v = 2v * 0.001

  = 0.002v

uncertainty in a nominal displacement

= (u^2 + v^2)^(1/2)

= ((0.01225)^2 + (0.002)^2)^(1/2)

= 0.0124 cm

Therefore, The Estimated uncertainty in a nominal displacement of 2 cm at the design stage is plus or minus 0.0124cm

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explanation: