Question

# 2.) Consider a Pt resistance sensor that requires long leads to operate. To compensate for the changes in the resistance of long leads, the sensor can be connected to a

Wheatstone bridge (as R1, see picture) using long leads (1,2,3) of same dimensions and material. They will all be subject to the same change in resistance (AR) due to temperature. If we consider lead #1 in series with R3 and lead #3 in series with R1, for R1 = R3 (and hence R2 = R4),starting from the general Wheatstone bridge output expression: \mathbf{V}_{\bullet}=\mathbf{V}_{\mathbf{A B}}-\mathbf{V}_{\mathbf{A D}}=\mathbf{V}_{\mathbf{2}}\left(\frac{\mathbf{R}_{\mathbf{1}}}{\mathbf{R}_{\mathbf{1}}+\mathbf{R}_{\mathbf{2}}}-\frac{\mathbf{R}_{\mathbf{3}}}{\mathbf{R}_{\mathbf{3}}+\mathbf{R}_{\mathbf{4}}}\right) show that the Wheatstone bridge cancels the effects of temperature on the long leads. In other words, show that V. = 0 when temperature varies and affects the resistance of the long leads.

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