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
Flow can be measured by ____.
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