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 ΩRₓBGACD40 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 40 cm from the left end A of the 100 cm wire. Find Rx.

R = 2 Ωl = 40 cmL = 100 cm
Rx = Ω
2.Easy
+−5 VR1​ = 200 ΩR2​ = 300 ΩR3​ = 50 ΩR4​ = 600 Ωab+−Vab​ = ?

Find the open-circuit output voltage Vab = Va − Vb of the bridge shown, with Vs = 5 V.

Vs = 5 VR1 = 200 ΩR2 = 300 ΩR3 = 50 ΩR4 = 600 Ω
Vab = V
3.Medium
+−2 V1000 Ω1000 Ω + ΔR1000 Ω1000 Ωab+−Vab​ = ?

A bridge has four 1000 Ω arms and Vs = 2 V. The sensor R₂ increases by ΔR = 10 Ω. Using the small-change approximation, find the output Vab in mV.

Vs = 2 VR = 1000 ΩΔR = 10 Ω
Vab = mV
4.Medium
+−3 V350 Ω350 Ω + ΔR350 Ω350 Ωab+−71.43 mV

A bridge with four 350 Ω arms is supplied with 3 V. When the sensor R₂ changes, the output reads Vab = 71.43 mV. Find the exact change ΔR of R₂.

Vs = 3 VR = 350 ΩVab = 71.43 mV
ΔR = Ω
5.Hard
+−10 V120 Ω − ΔR120 Ω + ΔR120 Ω + ΔR120 Ω − ΔRab+−Vo​ = ?

A load cell (a full bridge of strain gauges) has a rated output of 2.5 mV/V at its rated load of 200 kg. It is excited with 10 V. Find its output Vo under a load of 120 kg.

2.5 mV/VFrated = 200 kgVs = 10 VF = 120 kg
Vo = mV
6.Hard
+−5 V120 Ω − ΔR120 Ω + ΔR120 Ω120 Ωab+−Vo​ = ?

A bridge with 120 Ω arms is excited with 5 V and has two active gauges in adjacent arms, one in tension and one in compression (half bridge). The gauge factor is 2.05 and the strain is 1200 µε. Find the bridge output Vo in mV.

Vs = 5 VGF = 2.05ε = 1200 µε
Vo = mV

Answer key

  1. 1. Rx = 3 Ω
  2. 2. Vab = −1.615 V
  3. 3. Vab = 5 mV
  4. 4. ΔR = 35 Ω
  5. 5. Vo = 15 mV
  6. 6. Vo = 6.15 mV

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