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 = 500 Ω, R₂ = 800 Ω and R₃ = 800 Ω. Find the unknown resistor R₄.

R₁ = 500 ΩR₂ = 800 ΩR₃ = 800 Ω

R₄ = Ω

2.Easy

In a slide-wire (metre) bridge a known 50 Ω resistor sits in the left gap and an unknown resistor Rₓ in the right gap. The galvanometer reads zero when the jockey is 35 cm from the left end A of the 100 cm wire. Find R_x.

R = 50 Ωl = 35 cmL = 100 cm

R_x = Ω

3.Medium

A bridge has four 200 Ω arms and V_s = 12 V. The sensor R₂ increases by ΔR = 1.6 Ω. Using the small-change approximation, find the output V_ab in mV.

V_s = 12 VR = 200 ΩΔR = 1.6 Ω

V_ab = mV

4.Medium

A galvanometer with a resistance of 200 Ω is connected between a and b of the bridge shown (V_s = 6 V). Find the galvanometer current I_g from a to b, in µA.

V_s = 6 VR₁ = 150 ΩR₂ = 60 ΩR₃ = 1000 ΩR₄ = 10 ΩR_g = 200 Ω

I_g = µA

5.Hard

A bridge with 350 Ω arms is excited with 2.5 V and has one active gauge (quarter bridge). The gauge factor is 2.12 and the strain is 1200 µε. Find the bridge output V_o in mV.

V_s = 2.5 VGF = 2.12ε = 1200 µε

V_o = mV

6.Hard

A strain gauge (GF = 2.1) on a member with E = 210 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 = 210 GPa

σ = MPa

Answer key

1. R₄ = 1280 Ω
2. R_x = 92.86 Ω
3. V_ab = 24 mV
4. I_g = 6547 µA
5. V_o = 1.59 mV
6. σ = 42 MPa

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