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 = 5 V, R₁ = 60 Ω and R₂ = 40 Ω. Find the voltage V_a of node a with respect to the negative supply rail.

V_s = 5 VR₁ = 60 ΩR₂ = 40 ΩR₃ = 20 ΩR₄ = 100 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 25 cm from the left end A of the 100 cm wire. Find R_x.

R = 50 Ωl = 25 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 = 5 VR₁ = 400 ΩR₂ = 40 ΩR₃ = 800 ΩR₄ = 500 Ω

R_th = Ω

4.Medium

A bridge has four 400 Ω arms and V_s = 2 V. The sensor R₂ increases by ΔR = 1.6 Ω. Using the small-change approximation, find the output V_ab in mV.

V_s = 2 VR = 400 ΩΔR = 1.6 Ω

V_ab = mV

5.Hard

A quarter bridge (one active gauge, GF = 2.05) is excited with 2.5 V. The largest strain to be measured is 200 µε, and it must give 5 V at the input of an analogue-to-digital converter. Find the amplifier gain G.

V_s = 2.5 VGF = 2.05ε_max = 200 µεV_FS = 5 V

G =

6.Hard

A strain gauge (GF = 2.1) on a member with E = 110 GPa forms a quarter bridge excited with 3 V. The output reads 0.315 mV. Find the axial stress σ in MPa.

V_s = 3 VGF = 2.1V_o = 0.315 mVE = 110 GPa

σ = MPa

Answer key

1. V_a = 2 V
2. R_x = 150 Ω
3. R_th = 344.1 Ω
4. V_ab = 2 mV
5. G = 19512
6. σ = 22 MPa

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