Wheatstone bridge & strain gauges worksheet with answers

Free printable Wheatstone bridge & strain gauges worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

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1.Easy
20 ΩRₓBGACD30 cm

In a slide-wire (metre) bridge a known 20 Ω resistor sits in the left gap and an unknown resistor Rₓ in the right gap. The galvanometer reads zero when the jockey is 30 cm from the left end A of the 100 cm wire. Find Rx.

R = 20 Ωl = 30 cmL = 100 cm
Rx = Ω
2.Easy
20 ΩRₓBGACD65 cm

In a slide-wire (metre) bridge a known 20 Ω resistor sits in the left gap and an unknown resistor Rₓ in the right gap. The galvanometer reads zero when the jockey is 65 cm from the left end A of the 100 cm wire. Find Rx.

R = 20 Ωl = 65 cmL = 100 cm
Rx = Ω
3.Medium
+−2 V350 Ω350 Ω + ΔR350 Ω350 Ωab+−Vab​ = ?

A bridge has four 350 Ω arms and Vs = 2 V. The sensor R₂ increases by ΔR = 2.8 Ω. Using the small-change approximation, find the output Vab in mV.

Vs = 2 VR = 350 ΩΔR = 2.8 Ω
Vab = mV
4.Medium
+−10 V350 Ω350 Ω + ΔR350 Ω350 Ωab+−Vab​ = ?

A bridge has four 350 Ω arms and Vs = 10 V. The sensor R₂ increases by ΔR = 1.75 Ω. Using the small-change approximation, find the output Vab in mV.

Vs = 10 VR = 350 ΩΔR = 1.75 Ω
Vab = mV
5.Hard
+−3 V350 Ω350 Ω + ΔR350 Ω350 Ωab+−1.5 mV

A strain gauge (GF = 2) on a member with E = 110 GPa forms a quarter bridge excited with 3 V. The output reads 1.5 mV. Find the axial stress σ in MPa.

Vs = 3 VGF = 2Vo = 1.5 mVE = 110 GPa
σ = MPa
6.Hard
+−3 V350 Ω350 Ω + ΔR350 Ω350 Ωab+−1.59 mV

A quarter bridge with one active gauge (GF = 2.12) is excited with 3 V. Under load the output reads 1.59 mV. Find the strain ε in µε.

Vs = 3 VGF = 2.12Vo = 1.59 mV
ε = µε

Answer key

  1. 1. Rx = 46.67 Ω
  2. 2. Rx = 10.77 Ω
  3. 3. Vab = 4 mV
  4. 4. Vab = 12.5 mV
  5. 5. σ = 110 MPa
  6. 6. ε = 1000 µε

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