Let\'s start by assuming that RX= 1000, RA=2700?, RB=5400?, RC=1500?, and VS=24V
ID: 1927897 • Letter: L
Question
Let's start by assuming that RX= 1000, RA=2700?, RB=5400?, RC=1500?, and VS=24V. The change in resistance is very small: if the piece of steel the gauge is bonded to stretches by ?ll=0.001 the gauge increases resistance by only 2? 1) What is the output voltage vO, in Volts, if the gauge is not deformed? 2) Now suppose the gauge stretches so its resistance changes to RX=1002.0?. What is the change in the output voltage, in milliVolts? 3) We would really like the output voltage to be zero when the gauge is not deformed. Keeping the other resistors the same, what should we make the resistance RB to accomplish this? Express your answer in Ohms. Now we want to choose some resistances to get the maximum sensitivity: we want the biggest change in output voltage for a change in the gauge resistance. We also want the output voltage to be zero when the gauge is not deformed. 4) Assume that we are given RA=3000.0?, and remember that the nominal undeformed resistance of the gauge RX=1000?. What value should we choose for RC, in Ohms? 5) What value should we choose for RB, in Ohms?
Explanation / Answer
Solution
Vs=24V
Rx=1000
Ra=2700
Rb=5400
Rc=1500
Case 1
when there is no deformation.
Ra+Rb+Rc=2700+5400+1500(series)
Rtabc=9600
Rtabc are in parallel Rx=1000
by applying voltage divider to calculate current across
at Ra and Rb,
Vs=VtxRa/(Ra+Rb)
24=Vtx5400/(2700+5400)
Vt=36v
by applying voltage bivider at rb and rc
vt=voRc/(Rb+Rc)
36=Vo1500/(5400+1500)
vo=165V
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