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
+−15 VR1​ = 300 ΩR2​ = 600 ΩR3​ = 150 ΩR4​ = ?abG0

The Wheatstone bridge in the diagram is balanced: the galvanometer reads zero. R₁ = 300 Ω, R₂ = 600 Ω and R₃ = 150 Ω. Find the unknown resistor R4.

R1 = 300 ΩR2 = 600 ΩR3 = 150 Ω
R4 = Ω
2.Easy
10 ΩRₓBGACD60 cm

In a slide-wire (metre) bridge a known 10 Ω resistor sits in the left gap and an unknown resistor Rₓ in the right gap. The galvanometer reads zero when the jockey is 60 cm from the left end A of the 100 cm wire. Find Rx.

R = 10 Ωl = 60 cmL = 100 cm
Rx = Ω
3.Medium
+−5 V500 Ω500 Ω + ΔR500 Ω500 Ωab+−Vab​ = ?

A bridge has four 500 Ω arms and Vs = 5 V. The sensor R₂ increases by ΔR = 40 Ω. Find the exact output Vab in mV.

Vs = 5 VR = 500 ΩΔR = 40 Ω
Vab = mV
4.Medium
+−2 V1000 Ω1000 Ω1000 Ω1000 Ωab+−

A 1000 Ω strain gauge is one arm (R₂) of a bridge with four equal 1000 Ω arms and an excitation of 2 V. Find the power Pg dissipated in the gauge, in mW. Self-heating limits the excitation.

Vs = 2 VR = 1000 Ω
Pg = mW
5.Hard
+−10 V120 Ω120 Ω + ΔR120 Ω120 Ωab+−4.2 mV

A strain gauge (GF = 2.1) on a member with E = 200 GPa forms a quarter bridge excited with 10 V. The output reads 4.2 mV. Find the axial stress σ in MPa.

Vs = 10 VGF = 2.1Vo = 4.2 mVE = 200 GPa
σ = MPa
6.Hard
+−2.5 V120 Ω120 Ω + ΔR120 Ω120 Ωab+−0.32 mV

A quarter bridge with one active gauge (GF = 2.05) is excited with 2.5 V. Under load the output reads 0.32 mV. Find the strain ε in µε.

Vs = 2.5 VGF = 2.05Vo = 0.32 mV
ε = µε

Answer key

  1. 1. R4 = 300 Ω
  2. 2. Rx = 6.667 Ω
  3. 3. Vab = 96.15 mV
  4. 4. Pg = 1 mW
  5. 5. σ = 160 MPa
  6. 6. ε = 249.8 µε

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