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

The Wheatstone bridge in the diagram is balanced: the galvanometer reads zero. R₁ = 400 Ω, R₂ = 40 Ω and R₃ = 120 Ω. Find the unknown resistor R₄.

R₁ = 400 ΩR₂ = 40 ΩR₃ = 120 Ω

R₄ = Ω

2.Easy

The bridge shown is supplied with V_s = 12 V and its output is open. Find the current I_s drawn from the supply, in mA.

V_s = 12 VR₁ = 150 ΩR₂ = 400 ΩR₃ = 400 ΩR₄ = 60 Ω

I_s = mA

3.Medium

A bridge has four 1000 Ω arms and V_s = 3 V. The sensor R₂ increases by ΔR = 8 Ω. Using the small-change approximation, find the output V_ab in mV.

V_s = 3 VR = 1000 ΩΔR = 8 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 = 9 VR₁ = 150 ΩR₂ = 120 ΩR₃ = 100 ΩR₄ = 300 Ω

R_th = Ω

5.Hard

A bridge with 350 Ω arms is excited with 3 V and has two active gauges in adjacent arms, one in tension and one in compression (half bridge). The gauge factor is 2 and the strain is 400 µε. Find the bridge output V_o in mV.

V_s = 3 VGF = 2ε = 400 µε

V_o = mV

6.Hard

A strain gauge (GF = 2.1) on a member with E = 200 GPa forms a quarter bridge excited with 10 V. The output reads 1.05 mV. Find the axial stress σ in MPa.

V_s = 10 VGF = 2.1V_o = 1.05 mVE = 200 GPa

σ = MPa

Answer key

1. R₄ = 12 Ω
2. I_s = 47.91 mA
3. V_ab = 6 mV
4. R_th = 141.7 Ω
5. V_o = 1.2 mV
6. σ = 40 MPa

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