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
50 ΩRₓBGACD40 cm

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 40 cm from the left end A of the 100 cm wire. Find Rx.

R = 50 Ωl = 40 cmL = 100 cm
Rx = Ω
2.Easy
+−6 VR1​ = 300 ΩR2​ = 250 ΩR3​ = 300 ΩR4​ = ?abG0

The Wheatstone bridge in the diagram is balanced: the galvanometer reads zero. R₁ = 300 Ω, R₂ = 250 Ω and R₃ = 300 Ω. Find the unknown resistor R4.

R1 = 300 ΩR2 = 250 ΩR3 = 300 Ω
R4 = Ω
3.Medium
+−10 V200 Ω200 Ω + ΔR200 Ω200 Ωab+−Vab​ = ?

A bridge has four 200 Ω arms and Vs = 10 V. The sensor R₂ increases by ΔR = 16 Ω. Find the exact output Vab in mV.

Vs = 10 VR = 200 ΩΔR = 16 Ω
Vab = mV
4.Medium
+−5 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 5 V. Find the power Pg dissipated in the gauge, in mW. Self-heating limits the excitation.

Vs = 5 VR = 1000 Ω
Pg = mW
5.Hard
+−10 V120 Ω − ΔR120 Ω + ΔR120 Ω + ΔR120 Ω − ΔRab+−Vo​ = ?

A bridge with 120 Ω arms is excited with 10 V and has four active gauges, two in tension and two in compression (full bridge). The gauge factor is 2 and the strain is 750 µε. Find the bridge output Vo in mV.

Vs = 10 VGF = 2ε = 750 µε
Vo = mV
6.Hard
+−2.5 V120 Ω120 Ω + ΔR120 Ω120 Ωab+−0.313 mV

A strain gauge (GF = 2) on a member with E = 210 GPa forms a quarter bridge excited with 2.5 V. The output reads 0.313 mV. Find the axial stress σ in MPa.

Vs = 2.5 VGF = 2Vo = 0.313 mVE = 210 GPa
σ = MPa

Answer key

  1. 1. Rx = 75 Ω
  2. 2. R4 = 250 Ω
  3. 3. Vab = 192.3 mV
  4. 4. Pg = 6.25 mW
  5. 5. Vo = 15 mV
  6. 6. σ = 52.58 MPa

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