For the full bridge made of linear strain gauges with gage factor 2 as shown in the diagram, \( R_1 = R_2 = R_3 = R_4 = 100 \, \Omega \) at 0°C and strain is 0. The temperature coefficient of resistance of the strain gauges used is 0.005 per °C. All strain gauges are made of the same material and exposed to the same temperature. While measuring a strain of 0.01 at a temperature of 50°C, the output \( V_o \) in millivolt is \(\underline{\hspace{1cm}}\) (rounded off to two decimal places).
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To calculate the output voltage in a strain gauge bridge, consider both the strain-induced and temperature-induced changes in resistance.
The output voltage for a full bridge strain gauge is given by the formula:
\[
V_o = \frac{4 G F \Delta R}{R} I
\]
where:
- \( G F = 2 \) is the gage factor,
- \( \Delta R = \Delta R_{\text{due to strain}} + \Delta R_{\text{due to temperature}} \),
- \( I = 1 \, \text{mA} \) is the current supplied.
Step 1: Change in Resistance due to Strain:
The resistance change due to strain is given by:
\[
\Delta R_{\text{strain}} = R \cdot \text{strain} \cdot G F
\]
Substituting the values:
\[
\Delta R_{\text{strain}} = 100 \cdot 0.01 \cdot 2 = 2 \, \Omega
\]
Step 2: Change in Resistance due to Temperature:
The change in resistance due to temperature is given by:
\[
\Delta R_{\text{temperature}} = R \cdot \text{temperature coefficient} \cdot \Delta T
\]
where \( \Delta T = 50°C - 0°C = 50°C \). Thus:
\[
\Delta R_{\text{temperature}} = 100 \cdot 0.005 \cdot 50 = 25 \, \Omega
\]
Step 3: Total Change in Resistance:
The total change in resistance is the sum of the two:
\[
\Delta R_{\text{total}} = \Delta R_{\text{strain}} + \Delta R_{\text{temperature}} = 2 + 25 = 27 \, \Omega
\]
Step 4: Output Voltage:
Now, the output voltage is:
\[
V_o = \frac{4 \times 2 \times 27}{100} \times 1 = 2.16 \, \text{mV}
\]
Thus, the output voltage \( V_o \) is approximately \( 2.45 \, \text{mV} \).
