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

In the bridge shown, V_s = 12 V, R₁ = 1000 Ω and R₂ = 40 Ω. Find the voltage V_a of node a with respect to the negative supply rail.

V_s = 12 VR₁ = 1000 ΩR₂ = 40 ΩR₃ = 250 ΩR₄ = 300 Ω

V_a = V

2.Easy

In a slide-wire (metre) bridge a known 50 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 = 50 Ωl = 35 cmL = 100 cm

R_x = Ω

3.Medium

A bridge has four 120 Ω arms and V_s = 2 V. The sensor R₂ increases by ΔR = 0.96 Ω. Using the small-change approximation, find the output V_ab in mV.

V_s = 2 VR = 120 ΩΔR = 0.96 Ω

V_ab = mV

4.Medium

A bridge has four 330 Ω arms and V_s = 2 V. The sensor R₂ increases by ΔR = 3.3 Ω. Using the small-change approximation, find the output V_ab in mV.

V_s = 2 VR = 330 ΩΔR = 3.3 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 500 kg. It is excited with 5 V. Find its output V_o under a load of 250 kg.

2.5 mV/VF_rated = 500 kgV_s = 5 VF = 250 kg

V_o = mV

6.Hard

A quarter bridge (one active gauge, GF = 2.1) is excited with 3 V. The largest strain to be measured is 750 µε, and it must give 5 V at the input of an analogue-to-digital converter. Find the amplifier gain G.

V_s = 3 VGF = 2.1ε_max = 750 µεV_FS = 5 V

G =

Answer key

1. V_a = 0.4615 V
2. R_x = 92.86 Ω
3. V_ab = 4 mV
4. V_ab = 5 mV
5. V_o = 6.25 mV
6. G = 4233

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