The problem asks to calculate the strain in a cantilever element using active strain gauges arranged in a half-bridge configuration.
Half-Bridge Strain Gauge Formula
For a half-bridge configuration using two active strain gauges, where one experiences tensile strain ($\epsilon$) and the other experiences compressive strain ($-\epsilon$), the output voltage ($V_{out}$) is related to the supply voltage ($V_s$), gauge factor ($GF$), and strain ($\epsilon$) by the following approximate formula (valid for small strains):
$ V_{out} \approx - V_s \frac{GF \cdot \epsilon}{2} $
We are interested in the magnitude of the strain.
Calculating Strain
We can rearrange the formula to solve for strain ($\epsilon$):
$ \epsilon \approx \frac{2 \cdot |V_{out}|}{V_s \cdot GF} $
Input Values
- Supply Voltage ($V_s$): 10 V
- Output Voltage ($V_{out}$): 1 mV = $1 \times 10^{-3}$ V
- Gauge Factor ($GF$): 2.5
Substitution and Calculation
Substitute the given values into the rearranged formula:
$ \epsilon \approx \frac{2 \cdot (1 \times 10^{-3} \text{ V})}{10 \text{ V} \cdot 2.5} $
$ \epsilon \approx \frac{2 \times 10^{-3}}{25} $
$ \epsilon \approx 0.08 \times 10^{-3} $
$ \epsilon \approx 8 \times 10^{-5} $
Convert to Microstrain
Strain is often expressed in microstrain ($\mu\epsilon$), where $1 \mu\epsilon = 10^{-6}$.
$ \epsilon \approx 8 \times 10^{-5} = 80 \times 10^{-6} $
Therefore, the strain is approximately 80 microstrain.
Important Questions from Resistive Transducers
Which of the following is NOT an advantage of LVDT?
Flow can be measured by ____.
In the force transducer shown in Figure (a), four identical strain gauges S1, S2, S3, and S4 are mounted on a cantilever at equal distance from its base. S1 and S2 are mounted on the top surface and S3 and S4 are mounted on the bottom surface, as shown in the Figure (a). These strain gauges are to be connected to form a Wheatstone bridge consisting of four arms A, B, C, and D, as shown in the Figure (b). From the following options, the correct order to maximize the measurement sensitivity is
A metallic strain-gauge (SG) with resistance $R_{SG}$ is connected as shown in the figure, where $R_{L1}$, $R_{L2}$, $R_{L3}$ represent the lead wire resistances. The SG has a gauge factor of 2 and nominal resistance $R_N$ of 125 $\Omega$. When the SG is subjected to a tensile strain of $2 \times 10^{-3}$, the resulting change in $R_{SG}$ is $\Delta R$. The $\Delta R$ value is measured as $\Delta R_{MEAS} = R_{EQ2} - R_{EQ1}$. The $R_{EQ1}$ and $R_{EQ2}$ are the equivalent resistances measured between the terminals 1 and 2, and terminals 2 and 3, respectively.
If $R_{L1} = R_{L2} = 5 \ \Omega$, and $R_{L3} = 4.95 \ \Omega$, the measured value of tensile strain is ______ $\times 10^{-3}$ (rounded off to two decimal places).
- A wire-wound ‘resistive potentiometer type' angle sensor with 72 turns is used in an application. The first turn of the potentiometer is connected to ground while its last turn is connected to 3.6 V. The width of the wiper covers two turns ensuring make-before-break. The output (wiper) voltage when the wiper is on top of both the turns 35 and 36 is ________ V (rounded off to two decimal places).
