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
+−2 VR1​ = 50 ΩR2​ = 200 ΩR3​ = 120 ΩR4​ = ?abG0

The Wheatstone bridge in the diagram is balanced: the galvanometer reads zero. R₁ = 50 Ω, R₂ = 200 Ω and R₃ = 120 Ω. Find the unknown resistor R4.

R1 = 50 ΩR2 = 200 ΩR3 = 120 Ω
R4 = Ω
2.Easy
+−5 VR1​ = 10 ΩR2​ = 500 ΩR3​ = 80 ΩR4​ = ?abG0

The Wheatstone bridge in the diagram is balanced: the galvanometer reads zero. R₁ = 10 Ω, R₂ = 500 Ω and R₃ = 80 Ω. Find the unknown resistor R4.

R1 = 10 ΩR2 = 500 ΩR3 = 80 Ω
R4 = Ω
3.Medium
+−6 V150 Ω150 Ω + ΔR150 Ω150 Ωab+−Vab​ = ?

A bridge has four 150 Ω arms and Vs = 6 V. The sensor R₂ increases by ΔR = 1.5 Ω. Using the small-change approximation, find the output Vab in mV.

Vs = 6 VR = 150 ΩΔR = 1.5 Ω
Vab = mV
4.Medium
+−5 V220 Ω220 Ω + ΔR220 Ω220 Ωab+−96.15 mV

A bridge with four 220 Ω arms is supplied with 5 V. When the sensor R₂ changes, the output reads Vab = 96.15 mV. Find the exact change ΔR of R₂.

Vs = 5 VR = 220 ΩVab = 96.15 mV
ΔR = Ω
5.Hard
+−2.5 V1000 Ω1000 Ω + ΔR1000 Ω1000 Ωab+−0.32 mV

A strain gauge (GF = 2.05) on a member with E = 200 GPa forms a quarter bridge excited with 2.5 V. The output reads 0.32 mV. Find the axial stress σ in MPa.

Vs = 2.5 VGF = 2.05Vo = 0.32 mVE = 200 GPa
σ = MPa
6.Hard
+−2.5 V350 Ω350 Ω + ΔR350 Ω350 Ωab+−0.625 mV

A quarter bridge with one active gauge (GF = 2) is excited with 2.5 V. Under load the output reads 0.625 mV. Find the strain ε in µε.

Vs = 2.5 VGF = 2Vo = 0.625 mV
ε = µε

Answer key

  1. 1. R4 = 480 Ω
  2. 2. R4 = 4000 Ω
  3. 3. Vab = 15 mV
  4. 4. ΔR = 17.6 Ω
  5. 5. σ = 49.95 MPa
  6. 6. ε = 500 µε

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