A practical work order without difficult mathematics:
Wheatstone measuring bridge with strain gauge
The final inspection measures the mass m of the filled packages with a strain gauge built within a Wheatstone bridge. The strain gauge has a nominal resistance of R0 = 120 Ω. This changes by +- 10Ω for a change in length of 1μm. The installed strain gauge gets a change in length of 2μm per kg due to load. When the bridge is balanced, the flour package has the correct filling weight.
- By how many ohms does the installed strain gauge change its resistance value (ΔR) due to the mass m1 of 1 kg?
- What is the mass m2 of the filled package in kg when the bridge is balanced?
ΔR = +- 10Ω/μm … (1)
Δl = 2 μm/kg => Δl = 1 μm/0,5 kg … (2)
…(2) in …(1): ΔR = +- 10Ω/0,5 kg = +- 20 Ω/kg
Resistance of the strain gauge: ΔR (1 kg) = +- 20 Ω
Wheatstone bridge balanced, when strain gauge = 70 Ω => ΔR = R0 - ΔR = 70 Ω- 20 Ω = 50 Ω
20 Ω = 50 Ω => m2 = 50 Ω * 1 kg = 2,5 kg
1 kg m2 20 Ω