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 ΩRₓBGACD45 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 45 cm from the left end A of the 100 cm wire. Find Rx.

R = 100 Ωl = 45 cmL = 100 cm
Rx = Ω
2.Easy
+−3 VR1​ = 800 ΩR2​ = 150 ΩR3​ = 80 ΩR4​ = 100 Ωab+−Vab​ = ?

Find the open-circuit output voltage Vab = Va − Vb of the bridge shown, with Vs = 3 V.

Vs = 3 VR1 = 800 ΩR2 = 150 ΩR3 = 80 ΩR4 = 100 Ω
Vab = V
3.Medium
+−9 VR1​ = 50 ΩR2​ = 600 ΩR3​ = 60 ΩR4​ = 120 ΩabGRg​ = 50 Ω

A galvanometer with a resistance of 50 Ω is connected between a and b of the bridge shown (Vs = 9 V). Find the galvanometer current Ig from a to b, in µA.

Vs = 9 VR1 = 50 ΩR2 = 600 ΩR3 = 60 ΩR4 = 120 ΩRg = 50 Ω
Ig = µA
4.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 = 1.6 Ω. Using the small-change approximation, find the output Vab in mV.

Vs = 10 VR = 200 ΩΔR = 1.6 Ω
Vab = mV
5.Hard
+−3 V350 Ω350 Ω + ΔR350 Ω350 Ωab+−Vo​

A quarter bridge (one active gauge, GF = 2.1) is excited with 3 V. The largest strain to be measured is 1500 µε, and it must give 2.5 V at the input of an analogue-to-digital converter. Find the amplifier gain G.

Vs = 3 VGF = 2.1εmax = 1500 µεVFS = 2.5 V
G =
6.Hard
+−3 V120 Ω − ΔR120 Ω + ΔR120 Ω + ΔR120 Ω − ΔRab+−Vo​ = ?

A bridge with 120 Ω arms is excited with 3 V and has four active gauges, two in tension and two in compression (full bridge). The gauge factor is 2.05 and the strain is 1500 µε. Find the bridge output Vo in mV.

Vs = 3 VGF = 2.05ε = 1500 µε
Vo = mV

Answer key

  1. 1. Rx = 122.2 Ω
  2. 2. Vab = −1.193 V
  3. 3. Ig = 16949 µA
  4. 4. Vab = 20 mV
  5. 5. G = 1058
  6. 6. Vo = 9.225 mV

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