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
+−6 VR1​ = 800 ΩR2​ = 1000 ΩR3​ = 80 ΩR4​ = ?abG0

The Wheatstone bridge in the diagram is balanced: the galvanometer reads zero. R₁ = 800 Ω, R₂ = 1000 Ω and R₃ = 80 Ω. Find the unknown resistor R4.

R1 = 800 ΩR2 = 1000 ΩR3 = 80 Ω
R4 = Ω
2.Easy
+−9 VR1​ = 250 ΩR2​ = 80 ΩR3​ = 60 ΩR4​ = 400 Ωab+−

In the bridge shown, Vs = 9 V, R₁ = 250 Ω and R₂ = 80 Ω. Find the voltage Va of node a with respect to the negative supply rail.

Vs = 9 VR1 = 250 ΩR2 = 80 ΩR3 = 60 ΩR4 = 400 Ω
Va = V
3.Medium
+−6 V200 Ω200 Ω + ΔR200 Ω200 Ωab+−Vab​ = ?

A bridge has four 200 Ω arms and Vs = 6 V. The sensor R₂ increases by ΔR = 1.6 Ω. Using the small-change approximation, find the output Vab in mV.

Vs = 6 VR = 200 ΩΔR = 1.6 Ω
Vab = mV
4.Medium
+−10 V300 Ω300 Ω + ΔR300 Ω300 Ωab+−Vab​ = ?

A bridge has four 300 Ω arms and Vs = 10 V. The sensor R₂ increases by ΔR = 1.5 Ω. Using the small-change approximation, find the output Vab in mV.

Vs = 10 VR = 300 ΩΔR = 1.5 Ω
Vab = mV
5.Hard
+−3 V350 Ω350 Ω + ΔR350 Ω350 Ωab+−1.537 mV

A strain gauge (GF = 2.05) on a member with E = 70 GPa forms a quarter bridge excited with 3 V. The output reads 1.537 mV. Find the axial stress σ in MPa.

Vs = 3 VGF = 2.05Vo = 1.537 mVE = 70 GPa
σ = MPa
6.Hard
+−10 V350 Ω − ΔR350 Ω + ΔR350 Ω + ΔR350 Ω − ΔRab+−Vo​ = ?

A bridge with 350 Ω arms is excited with 10 V and has four active gauges, two in tension and two in compression (full bridge). The gauge factor is 2.12 and the strain is 250 µε. Find the bridge output Vo in mV.

Vs = 10 VGF = 2.12ε = 250 µε
Vo = mV

Answer key

  1. 1. R4 = 100 Ω
  2. 2. Va = 2.182 V
  3. 3. Vab = 12 mV
  4. 4. Vab = 12.5 mV
  5. 5. σ = 69.98 MPa
  6. 6. Vo = 5.3 mV

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