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 = 10 Ω, R₂ = 150 Ω and R₃ = 40 Ω. Find the unknown resistor R₄.

R₁ = 10 ΩR₂ = 150 ΩR₃ = 40 Ω

R₄ = Ω

2.Easy

In a slide-wire (metre) bridge a known 20 Ω resistor sits in the left gap and an unknown resistor Rₓ in the right gap. The galvanometer reads zero when the jockey is 80 cm from the left end A of the 100 cm wire. Find R_x.

R = 20 Ωl = 80 cmL = 100 cm

R_x = Ω

3.Medium

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

V_s = 3 VR₁ = 20 ΩR₂ = 150 ΩR₃ = 200 ΩR₄ = 60 Ω

R_th = Ω

4.Medium

A bridge has four 150 Ω arms and V_s = 15 V. The sensor R₂ increases by ΔR = 0.15 Ω. Using the small-change approximation, find the output V_ab in mV.

V_s = 15 VR = 150 ΩΔR = 0.15 Ω

V_ab = mV

5.Hard

A load cell (a full bridge of strain gauges) has a rated output of 2.5 mV/V at its rated load of 100 kg. It is excited with 5 V. Find its output V_o under a load of 60 kg.

2.5 mV/VF_rated = 100 kgV_s = 5 VF = 60 kg

V_o = mV

6.Hard

A bridge with 350 Ω arms is excited with 10 V and has four active gauges, two in tension and two in compression (full bridge). The gauge factor is 2 and the strain is 600 µε. Find the bridge output V_o in mV.

V_s = 10 VGF = 2ε = 600 µε

V_o = mV

Answer key

1. R₄ = 600 Ω
2. R_x = 5 Ω
3. R_th = 63.8 Ω
4. V_ab = 3.75 mV
5. V_o = 7.5 mV
6. V_o = 12 mV

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