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 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 75 cm from the left end A of the 100 cm wire. Find R_x.

R = 50 Ωl = 75 cmL = 100 cm

R_x = Ω

2.Easy

Find the open-circuit output voltage V_ab = V_a − V_b of the bridge shown, with V_s = 6 V.

V_s = 6 VR₁ = 120 ΩR₂ = 1000 ΩR₃ = 500 ΩR₄ = 250 Ω

V_ab = V

3.Medium

A galvanometer with a resistance of 20 Ω is connected between a and b of the bridge shown (V_s = 2 V). Find the galvanometer current I_g from a to b, in µA.

V_s = 2 VR₁ = 80 ΩR₂ = 800 ΩR₃ = 20 ΩR₄ = 300 ΩR_g = 20 Ω

I_g = µA

4.Medium

A bridge has four 500 Ω arms and V_s = 15 V. The sensor R₂ increases by ΔR = 2 Ω. Using the small-change approximation, find the output V_ab in mV.

V_s = 15 VR = 500 ΩΔR = 2 Ω

V_ab = mV

5.Hard

A quarter bridge (one active gauge, GF = 2) is excited with 5 V. The largest strain to be measured is 800 µε, and it must give 5 V at the input of an analogue-to-digital converter. Find the amplifier gain G.

V_s = 5 VGF = 2ε_max = 800 µεV_FS = 5 V

G =

6.Hard

A bridge with 350 Ω arms is excited with 3 V and has one active gauge (quarter bridge). The gauge factor is 2.1 and the strain is 1200 µε. Find the bridge output V_o in mV.

V_s = 3 VGF = 2.1ε = 1200 µε

V_o = mV

Answer key

1. R_x = 16.67 Ω
2. V_ab = 3.357 V
3. I_g = −509.7 µA
4. V_ab = 15 mV
5. G = 2500
6. V_o = 1.89 mV

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