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
100 ΩRₓBGACD70 cm

In a slide-wire (metre) bridge a known 100 Ω resistor sits in the left gap and an unknown resistor Rₓ in the right gap. The galvanometer reads zero when the jockey is 70 cm from the left end A of the 100 cm wire. Find Rx.

R = 100 Ωl = 70 cmL = 100 cm
Rx = Ω
2.Easy
10 ΩRₓBGACD20 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 20 cm from the left end A of the 100 cm wire. Find Rx.

R = 10 Ωl = 20 cmL = 100 cm
Rx = Ω
3.Medium
+−12 V220 Ω220 Ω + ΔR220 Ω220 Ωab+−Vab​ = ?

A bridge has four 220 Ω arms and Vs = 12 V. The sensor R₂ increases by ΔR = 0.88 Ω. Using the small-change approximation, find the output Vab in mV.

Vs = 12 VR = 220 ΩΔR = 0.88 Ω
Vab = mV
4.Medium
+−5 V150 Ω150 Ω + ΔR150 Ω150 Ωab+−60.98 mV

A bridge with four 150 Ω arms is supplied with 5 V. When the sensor R₂ changes, the output reads Vab = 60.98 mV. Find the exact change ΔR of R₂.

Vs = 5 VR = 150 ΩVab = 60.98 mV
ΔR = Ω
5.Hard
+−12 V120 Ω − ΔR120 Ω + ΔR120 Ω + ΔR120 Ω − ΔRab+−Vo​ = ?

A load cell (a full bridge of strain gauges) has a rated output of 1 mV/V at its rated load of 500 kg. It is excited with 12 V. Find its output Vo under a load of 200 kg.

1 mV/VFrated = 500 kgVs = 12 VF = 200 kg
Vo = mV
6.Hard
+−3 V350 Ω350 Ω + ΔR350 Ω350 Ωab+−1.125 mV

A quarter bridge with one active gauge (GF = 2) is excited with 3 V. Under load the output reads 1.125 mV. Find the strain ε in µε.

Vs = 3 VGF = 2Vo = 1.125 mV
ε = µε

Answer key

  1. 1. Rx = 42.86 Ω
  2. 2. Rx = 40 Ω
  3. 3. Vab = 12 mV
  4. 4. ΔR = 7.501 Ω
  5. 5. Vo = 4.8 mV
  6. 6. ε = 750 µε

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