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 = 120 Ω and R₃ = 80 Ω. Find the unknown resistor R₄.

R₁ = 400 ΩR₂ = 120 ΩR₃ = 80 Ω

R₄ = Ω

2.Easy

In the bridge shown, V_s = 6 V, R₁ = 60 Ω and R₂ = 50 Ω. Find the voltage V_a of node a with respect to the negative supply rail.

V_s = 6 VR₁ = 60 ΩR₂ = 50 ΩR₃ = 800 ΩR₄ = 500 Ω

V_a = V

3.Medium

Find the Thévenin resistance R_th of the bridge shown, seen from the output terminals a and b.

V_s = 9 VR₁ = 800 ΩR₂ = 150 ΩR₃ = 500 ΩR₄ = 1000 Ω

R_th = Ω

4.Medium

A bridge has four 500 Ω arms and V_s = 5 V. The sensor R₂ increases by ΔR = 4 Ω. Using the small-change approximation, find the output V_ab in mV.

V_s = 5 VR = 500 ΩΔR = 4 Ω

V_ab = mV

5.Hard

A 1000 Ω strain gauge with gauge factor 2 is bonded to a steel bar. Under load its resistance rises by 0.8 Ω. Find the strain ε in microstrain (µε).

R = 1000 ΩGF = 2ΔR = 0.8 Ω

ε = µε

6.Hard

A bridge with 120 Ω arms is excited with 2.5 V and has four active gauges, two in tension and two in compression (full bridge). The gauge factor is 2 and the strain is 250 µε. Find the bridge output V_o in mV.

V_s = 2.5 VGF = 2ε = 250 µε

V_o = mV

Answer key

1. R₄ = 24 Ω
2. V_a = 2.727 V
3. R_th = 459.6 Ω
4. V_ab = 10 mV
5. ε = 400 µε
6. V_o = 1.25 mV

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