Example 1 A resistance strain gauge is mounted on an Aluminum column with cross section 5 cm² if the strain gauge is connected to a Wheatstone bridge in place of R1 the Wheatstone has input voltage of 10V and initial resistance values of 4k. if the strain gouge has a gauge factor on 2.5 answer the following: Assuming linear behavior: 1. Define the output voltage as a relation with input force. 2. Define the overall sensitivity of the system. 3. If an input loaf of 10kN. 4. For an output voltage of 5mV calculate input force. 5. Calculate the error in 4 resulting from linear assumption. Example 2 A capacitive sensor used to measure water level is constructed using two coaxial tubes as shown, the sensor is connected to an AC Wheatstone bridge with R1-R2=50002 and input voltage 20V if the max. water level is 2m solve the following: 1. Define capacitance relation with water level. 2. What is the capacitance initial value (when the tank is empty)? 3. Define the output voltage as a function of input water level(x). 4. Calculate the output voltage range. 5. Calculate the output voltage for a water level of im Example3 The following deflection bridge is used to measure Torque input, if it has the following configuration solve questions a. and b.: R, is a rotary potentiometer with a full value of 9000 and having a sensitivity of 2.5n/" R₁ R₁ = R₁ =9kn and v = 10 V a. If R,had an initial rotation of 10° calculate R, at null position b. If R, was placed at the end of a 0.5 m long steel shaft with r=5cm as shown define the relation between input torque and output voltage T = f(v.) (assume linear bridge) Recall: ===78GPa Example4 A pressure-measuring device was constructed using a bellow pressure transducer and its tip displacement was measured using a linear potentiometer as shown. If relation between the bellow tip displacement (x) and the input pressure (p) is given as: x=k,p,, were k, is a constant and its value is 1.5 x 10"*m/Pa R₁ www R T(N.m) and the potentiometer has a sensitivity of 1000 /m and it was measured to be (10 cm) in length, the bellow is placed at a surrounding pressure of 1 Parm and the input voltage for the potentiometer was equal to 1V. For ease of calculation, assume 1p. = 10 pa Find the following: 1. Based on the drawn configuration this device will measure a. Absolute pressure b.positive gauge pressure c.negative gauge pressure (vacuum) d.any type of applied pressure 2. If v, is measured and found to be equal to 0.25 V calculate the input pressure in (pa) 3. Define the sensitivity of the whole system in unit of (m//pa) 4. calculate the minimum input pressure which can be measured using this device (hint: it will correspond to the maximum deflection) Example 5 A pressure measurement device constructed using a bellow (elastic element which extends when pressure is applied) and a potentiometer connected at its end to measure the resulting extension as shown. Knowing the following requirements choose a suitable input voltage 2. Define the overall sensitivity of the system. 3. If an input loaf of 10kN. 4. For an output voltage of 5mV calculate input force. 5. Calculate the error in 4 resulting from linear assumption. Example 2 A capacitive sensor used to measure water level is constructed using two coaxial tubes as shown, the sensor is connected to an AC Wheatstone bridge with R1-R2-50002 and input voltage 20V if the max. water level is am solve the following: 1. Define capacitance relation with water level. 2. What is the capacitance initial value (when the tank is empty)? 3. Define the output voltage as a function of input water level(x). 4. Calculate the output voltage range. 5. Calculate the output voltage for a water level of im Examples The following deflection bridge is used to measure Torque input, if it has the following configuration solve questions a. and b.: R, is a rotary potentiometer with a full value of 9000 and having a sensitivity of 2.5 n/ R₁ = R₁ = 9k and 10 V a. If R,had an initial rotation of 10" calculate R, at null position b. If R, was placed at the end of a 0.5 m long steel shaft with r=5cm as shown define the relation between input torque and output voltage T = f(v) (assume linear bridge) Recall: = G78GPa R, T(Nm) Example4 A pressure-measuring device was constructed using a bellow pressure transducer and its tip displacement was measured using a linear potentiometer as shown. If relation between the bellow tip displacement (x) and the input pressure (p)) is given as: x=k,p,, were k, is a constant and its value is 1.5 x 10""m/Pa and the potentiometer has a sensitivity of 1000 /m and it was measured to be (10 cm) in length, the bellow is placed at a surrounding pressure of 1 Pam and the input voltage for the potentiometer was equal to 1V. For ease of calculation, assume 1p.... = 10 pa Find the following: 1. Based on the drawn configuration this device will measure a. Absolute pressure b.positive gauge pressure R ww c.negative gauge pressure (vacuum) dany type of applied pressure 2. If v, is measured and found to be equal to 0.25 V calculate the input pressure in (pa) 3. Define the sensitivity of the whole system in unit of (mV/pa) 4 calculate the minimum input pressure which can be measured using this device (hint: it will correspond to the maximum deflection) P Example 5 A pressure measurement device constructed using a bellow (elastic element which extends when pressure is applied) and a potentiometer connected at its end to measure the resulting extension as shown, Knowing the following requirements choose a suitable input voltage source, potentiometer resistance, and bellow stiffness to operate the system correctly 1. Maximum allowable extension within bellow casing is 3 cm. 2. The voltmeter can handle a maximum current of 5 mA. 3. Pressure range is 0 -3.5 bar. 4. Based on your answers above write a direct relation between input pressure and output voltage. (v, as a function of pressure P).