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
2 ΩRₓBGACD65 cm

In a slide-wire (metre) bridge a known 2 Ω resistor sits in the left gap and an unknown resistor Rₓ in the right gap. The galvanometer reads zero when the jockey is 65 cm from the left end A of the 100 cm wire. Find Rx.

R = 2 Ωl = 65 cmL = 100 cm
Rx = Ω
2.Easy
+−6 VR1​ = 50 ΩR2​ = 100 ΩR3​ = 80 ΩR4​ = 80 Ωab+−

In the bridge shown, Vs = 6 V, R₁ = 50 Ω and R₂ = 100 Ω. Find the voltage Va of node a with respect to the negative supply rail.

Vs = 6 VR1 = 50 ΩR2 = 100 ΩR3 = 80 ΩR4 = 80 Ω
Va = V
3.Medium
+−6 V350 Ω350 Ω350 Ω350 Ωab+−

A 350 Ω strain gauge is one arm (R₂) of a bridge with four equal 350 Ω arms and an excitation of 6 V. Find the power Pg dissipated in the gauge, in mW. Self-heating limits the excitation.

Vs = 6 VR = 350 Ω
Pg = mW
4.Medium
+−6 V400 Ω400 Ω + ΔR400 Ω400 Ωab+−Vab​ = ?

A bridge has four 400 Ω arms and Vs = 6 V. The sensor R₂ increases by ΔR = 0.8 Ω. Using the small-change approximation, find the output Vab in mV.

Vs = 6 VR = 400 ΩΔR = 0.8 Ω
Vab = mV
5.Hard
+−3 V1000 Ω1000 Ω + ΔR1000 Ω1000 Ωab+−0.788 mV

A strain gauge (GF = 2.1) on a member with E = 210 GPa forms a quarter bridge excited with 3 V. The output reads 0.788 mV. Find the axial stress σ in MPa.

Vs = 3 VGF = 2.1Vo = 0.788 mVE = 210 GPa
σ = MPa
6.Hard
+−2.5 V120 Ω120 Ω + ΔR120 Ω120 Ωab+−Vo​ = ?

A bridge with 120 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 400 µε. Find the bridge output Vo in mV.

Vs = 2.5 VGF = 2.12ε = 400 µε
Vo = mV

Answer key

  1. 1. Rx = 1.077 Ω
  2. 2. Va = 4 V
  3. 3. Pg = 25.71 mW
  4. 4. Vab = 3 mV
  5. 5. σ = 105.1 MPa
  6. 6. Vo = 0.53 mV

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