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 = 1000 Ω, R₂ = 150 Ω and R₃ = 400 Ω. Find the unknown resistor R₄.

R₁ = 1000 ΩR₂ = 150 ΩR₃ = 400 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 35 cm from the left end A of the 100 cm wire. Find R_x.

R = 20 Ωl = 35 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 = 10 VR₁ = 60 ΩR₂ = 150 ΩR₃ = 1000 ΩR₄ = 20 Ω

R_th = Ω

4.Medium

A bridge has four 400 Ω arms and V_s = 10 V. The sensor R₂ increases by ΔR = 2 Ω. Using the small-change approximation, find the output V_ab in mV.

V_s = 10 VR = 400 ΩΔR = 2 Ω

V_ab = mV

5.Hard

A quarter bridge (one active gauge, GF = 2) 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.

V_s = 3 VGF = 2ε_max = 1500 µεV_FS = 2.5 V

G =

6.Hard

A bridge with 350 Ω arms is excited with 5 V and has one active gauge (quarter bridge). The gauge factor is 2.1 and the strain is 750 µε. Find the bridge output V_o in mV.

V_s = 5 VGF = 2.1ε = 750 µε

V_o = mV

Answer key

1. R₄ = 60 Ω
2. R_x = 37.14 Ω
3. R_th = 62.46 Ω
4. V_ab = 12.5 mV
5. G = 1111
6. V_o = 1.969 mV

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