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

Find the open-circuit output voltage V_ab = V_a − V_b of the bridge shown, with V_s = 6 V.

V_s = 6 VR₁ = 800 ΩR₂ = 500 ΩR₃ = 10 ΩR₄ = 150 Ω

V_ab = V

2.Easy

The Wheatstone bridge in the diagram is balanced: the galvanometer reads zero. R₁ = 800 Ω, R₂ = 150 Ω and R₃ = 120 Ω. Find the unknown resistor R₄.

R₁ = 800 ΩR₂ = 150 ΩR₃ = 120 Ω

R₄ = Ω

3.Medium

A bridge has four 300 Ω arms and V_s = 5 V. The sensor R₂ increases by ΔR = 15 Ω. Find the exact output V_ab in mV.

V_s = 5 VR = 300 ΩΔR = 15 Ω

V_ab = mV

4.Medium

Find the Thévenin resistance R_th of the bridge shown, seen from the output terminals a and b.

V_s = 5 VR₁ = 500 ΩR₂ = 300 ΩR₃ = 400 ΩR₄ = 600 Ω

R_th = Ω

5.Hard

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 800 µε. Find the bridge output V_o in mV.

V_s = 10 VGF = 2.12ε = 800 µε

V_o = mV

6.Hard

A strain gauge (GF = 2) on a member with E = 110 GPa forms a quarter bridge excited with 10 V. The output reads 1 mV. Find the axial stress σ in MPa.

V_s = 10 VGF = 2V_o = 1 mVE = 110 GPa

σ = MPa

Answer key

1. V_ab = −3.317 V
2. R₄ = 22.5 Ω
3. V_ab = 60.98 mV
4. R_th = 427.5 Ω
5. V_o = 16.96 mV
6. σ = 22 MPa

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