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

The Wheatstone bridge in the diagram is balanced: the galvanometer reads zero. R₁ = 400 Ω, R₂ = 100 Ω and R₃ = 80 Ω. Find the unknown resistor R₄.

R₁ = 400 ΩR₂ = 100 ΩR₃ = 80 Ω

R₄ = Ω

2.Easy

Find the open-circuit output voltage V_ab = V_a − V_b of the bridge shown, with V_s = 6 V.

V_s = 6 VR₁ = 400 ΩR₂ = 50 ΩR₃ = 1000 ΩR₄ = 80 Ω

V_ab = V

3.Medium

A bridge with four 400 Ω arms is supplied with 10 V. When the sensor R₂ changes, the output reads V_ab = 283 mV. Find the exact change ΔR of R₂.

V_s = 10 VR = 400 ΩV_ab = 283 mV

ΔR = Ω

4.Medium

A bridge has four 1000 Ω arms and V_s = 3 V. The sensor R₂ increases by ΔR = 80 Ω. Find the exact output V_ab in mV.

V_s = 3 VR = 1000 ΩΔR = 80 Ω

V_ab = mV

5.Hard

A load cell (a full bridge of strain gauges) has a rated output of 2 mV/V at its rated load of 50 kg. It is excited with 12 V. Find its output V_o under a load of 40 kg.

2 mV/VF_rated = 50 kgV_s = 12 VF = 40 kg

V_o = mV

6.Hard

A 120 Ω strain gauge with gauge factor 2.1 is bonded to a steel bar. Under load its resistance rises by 0.126 Ω. Find the strain ε in microstrain (µε).

R = 120 ΩGF = 2.1ΔR = 0.126 Ω

ε = µε

Answer key

1. R₄ = 20 Ω
2. V_ab = 0.2222 V
3. ΔR = 48 Ω
4. V_ab = 57.69 mV
5. V_o = 19.2 mV
6. ε = 500 µε

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