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 5 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 = 5 Ωl = 80 cmL = 100 cm

R_x = Ω

2.Easy

The Wheatstone bridge in the diagram is balanced: the galvanometer reads zero. R₁ = 250 Ω, R₂ = 40 Ω and R₃ = 40 Ω. Find the unknown resistor R₄.

R₁ = 250 ΩR₂ = 40 ΩR₃ = 40 Ω

R₄ = Ω

3.Medium

A bridge with four 220 Ω arms is supplied with 5 V. When the sensor R₂ changes, the output reads V_ab = 24.75 mV. Find the exact change ΔR of R₂.

V_s = 5 VR = 220 ΩV_ab = 24.75 mV

ΔR = Ω

4.Medium

A galvanometer with a resistance of 200 Ω is connected between a and b of the bridge shown (V_s = 6 V). Find the galvanometer current I_g from a to b, in µA.

V_s = 6 VR₁ = 20 ΩR₂ = 120 ΩR₃ = 10 ΩR₄ = 600 ΩR_g = 200 Ω

I_g = µA

5.Hard

A strain gauge (GF = 2.12) on a member with E = 210 GPa forms a quarter bridge excited with 10 V. The output reads 5.3 mV. Find the axial stress σ in MPa.

V_s = 10 VGF = 2.12V_o = 5.3 mVE = 210 GPa

σ = MPa

6.Hard

A load cell (a full bridge of strain gauges) has a rated output of 1.5 mV/V at its rated load of 100 kg. It is excited with 5 V. Find its output V_o under a load of 80 kg.

1.5 mV/VF_rated = 100 kgV_s = 5 VF = 80 kg

V_o = mV

Answer key

1. R_x = 1.25 Ω
2. R₄ = 6.4 Ω
3. ΔR = 4.4 Ω
4. I_g = −3343 µA
5. σ = 210 MPa
6. V_o = 6 mV

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