Question

: Suppose you’re trying to measure an unknown sensor resistance, ????????????????????o???? , by converting it to a voltage. For a fixed set of values of ????1 ,????1 ,???????????? and ????????????, each of the following circuits will yield an output voltage, ????o , as function of ????????????????????o???? . a. [10 points] For each of these circuits, write the equations relating ????o to ????????????????????o???? . b. [10 points] Find the sensitivity for each of these circuits (note that the sensitivities for some of these circuits may not be constants).

Answer 1

Answer:

(a) R₁ / (R₁ + $R_{sensor}$)

(b) -$R_{sensor}$ / (R₁ + $R_{sensor}$)

Explanation:

(a)

i - Using voltage division rule =

v₀ = v₁ [$R_{sensor}$ / (R₁+$R_{sensor}$)]

The sensitivity is

ii - $\int\limits^{vo}_{Rsensor}$ = dv₀/d$R_{sensor}$  *  $R_{sensor}$/v₀

                = R₁ / (R₁ + $R_{sensor}$)

(b)

i - Using voltage divisor rule = v₀ = v₁ [$R_{sensor}$ / (R₁+$R_{sensor}$)]

ii - $\int\limits^{vo}_{Rsensor}$ =  dv₀/d$R_{sensor}$  *  $R_{sensor}$/v₀

               = -$R_{sensor}$ / (R₁ + $R_{sensor}$)