Question

. a wheatstone bridge is formed by 1 strain gauge (r1) and three resistors (r2, r3, and r4). the initial resistance of all of them is the same 120 ohm. the gauge factor of the strain gauge (gf) is 1.5. the applied voltage (ei) on the wheatstone bridge is 10 v. initially, the bridge is balanced. after the strain gauge deforms, the bridge output (de0) is 10 mv. what is the strain?

Answer 1

The strain gauge's resistance changes due to deformation, causing an unbalance in the Wheatstone bridge circuit. The strain can be calculated using the following formula:

Strain = (De0 / GF) * (R2 / (R2 + R4))

Where:
- De0 is the output voltage of the Wheatstone bridge in millivolts (10 mV in this case)
- GF is the gauge factor of the strain gauge (1.5 in this case)
- R2 is the resistance of one of the three resistors in the Wheatstone bridge circuit (120 ohms in this case)
- R4 is the resistance of the strain gauge when it is deformed.

To calculate R4, we can use the formula for the resistance change of a strain gauge:

∆R/R = GF * Strain

Where:
- ∆R is the change in resistance of the strain gauge
- R is the initial resistance of the strain gauge (120 ohms in this case)
- GF is the gauge factor of the strain gauge (1.5 in this case)
- Strain is the strain applied to the strain gauge (unknown)

Rearranging the formula, we get:

∆R = R * GF * Strain

The resistance of the strain gauge when it is deformed (R4) can be calculated as:

R4 = R + ∆R

Substituting the values in the formulas, we get:

∆R = 120 ohms * 1.5 * Strain = 180 * Strain ohms
R4 = 120 ohms + 180 * Strain ohms = 120 + 0.18 * Strain kohms

Now we can substitute R4 and the other values in the formula for strain:

Strain = (De0 / GF) * (R2 / (R2 + R4))
Strain = (10 mV / 1.5) * (120 ohms / (120 ohms + 0.18 * Strain kohms))

Simplifying and solving for Strain, we get:

Strain = 1.8519 * 10^-4

Therefore, the strain is about 0.185%.