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
+−10 VR1​ = 800 ΩR2​ = 80 ΩR3​ = ?R4​ = 200 ΩabG0

The Wheatstone bridge in the diagram is balanced by adjusting R₃. R₁ = 800 Ω, R₂ = 80 Ω and R₄ = 200 Ω. Find the setting R3.

R1 = 800 ΩR2 = 80 ΩR4 = 200 Ω
R3 = Ω
2.Easy
20 ΩRₓBGACD55 cm

In a slide-wire (metre) bridge a known 20 Ω resistor sits in the left gap and an unknown resistor Rₓ in the right gap. The galvanometer reads zero when the jockey is 55 cm from the left end A of the 100 cm wire. Find Rx.

R = 20 Ωl = 55 cmL = 100 cm
Rx = Ω
3.Medium
+−12 V400 Ω400 Ω + ΔR400 Ω400 Ωab+−Vab​ = ?

A bridge has four 400 Ω arms and Vs = 12 V. The sensor R₂ increases by ΔR = 40 Ω. Find the exact output Vab in mV.

Vs = 12 VR = 400 ΩΔR = 40 Ω
Vab = mV
4.Medium
+−3 V120 Ω120 Ω120 Ω120 Ωab+−

A 120 Ω strain gauge is one arm (R₂) of a bridge with four equal 120 Ω arms and an excitation of 3 V. Find the power Pg dissipated in the gauge, in mW. Self-heating limits the excitation.

Vs = 3 VR = 120 Ω
Pg = mW
5.Hard
+−3 V120 Ω120 Ω + ΔR120 Ω120 Ωab+−Vo​

A quarter bridge (one active gauge, GF = 2.12) is excited with 3 V. The largest strain to be measured is 250 µε, and it must give 10 V at the input of an analogue-to-digital converter. Find the amplifier gain G.

Vs = 3 VGF = 2.12εmax = 250 µεVFS = 10 V
G =
6.Hard
+−3 V350 Ω350 Ω + ΔR350 Ω350 Ωab+−1.125 mV

A strain gauge (GF = 2) on a member with E = 210 GPa forms a quarter bridge excited with 3 V. The output reads 1.125 mV. Find the axial stress σ in MPa.

Vs = 3 VGF = 2Vo = 1.125 mVE = 210 GPa
σ = MPa

Answer key

  1. 1. R3 = 2000 Ω
  2. 2. Rx = 16.36 Ω
  3. 3. Vab = 285.7 mV
  4. 4. Pg = 18.75 mW
  5. 5. G = 25157
  6. 6. σ = 157.5 MPa

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