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

In the bridge shown, V_s = 2 V, R₁ = 60 Ω and R₂ = 250 Ω. Find the voltage V_a of node a with respect to the negative supply rail.

V_s = 2 VR₁ = 60 ΩR₂ = 250 ΩR₃ = 10 ΩR₄ = 50 Ω

V_a = V

2.Easy

The Wheatstone bridge in the diagram is balanced: the galvanometer reads zero. R₁ = 80 Ω, R₂ = 400 Ω and R₃ = 500 Ω. Find the unknown resistor R₄.

R₁ = 80 ΩR₂ = 400 ΩR₃ = 500 Ω

R₄ = Ω

3.Medium

A bridge has four 330 Ω arms and V_s = 15 V. The sensor R₂ increases by ΔR = 1.32 Ω. Using the small-change approximation, find the output V_ab in mV.

V_s = 15 VR = 330 ΩΔR = 1.32 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 = 10 VR₁ = 100 ΩR₂ = 800 ΩR₃ = 250 ΩR₄ = 600 Ω

R_th = Ω

5.Hard

A 1000 Ω strain gauge with gauge factor 2 is bonded to a steel bar. Under load its resistance rises by 3 Ω. Find the strain ε in microstrain (µε).

R = 1000 ΩGF = 2ΔR = 3 Ω

ε = µε

6.Hard

A strain gauge (GF = 2.12) on a member with E = 110 GPa forms a quarter bridge excited with 5 V. The output reads 1.06 mV. Find the axial stress σ in MPa.

V_s = 5 VGF = 2.12V_o = 1.06 mVE = 110 GPa

σ = MPa

Answer key

1. V_a = 1.613 V
2. R₄ = 2500 Ω
3. V_ab = 15 mV
4. R_th = 265.4 Ω
5. ε = 1500 µε
6. σ = 44 MPa

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