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 = 500 Ω, R₂ = 400 Ω and R₃ = 800 Ω. Find the unknown resistor R₄.

R₁ = 500 ΩR₂ = 400 ΩR₃ = 800 Ω

R₄ = Ω

2.Easy

In a slide-wire (metre) bridge a known 10 Ω resistor sits in the left gap and an unknown resistor Rₓ in the right gap. The galvanometer reads zero when the jockey is 30 cm from the left end A of the 100 cm wire. Find R_x.

R = 10 Ωl = 30 cmL = 100 cm

R_x = Ω

3.Medium

A galvanometer with a resistance of 200 Ω is connected between a and b of the bridge shown (V_s = 15 V). Find the galvanometer current I_g from a to b, in µA.

V_s = 15 VR₁ = 1000 ΩR₂ = 10 ΩR₃ = 200 ΩR₄ = 300 ΩR_g = 200 Ω

I_g = µA

4.Medium

Find the Thévenin resistance R_th of the bridge shown, seen from the output terminals a and b.

V_s = 6 VR₁ = 120 ΩR₂ = 100 ΩR₃ = 100 ΩR₄ = 1000 Ω

R_th = Ω

5.Hard

A 350 Ω strain gauge with gauge factor 2.12 is bonded to a steel bar. Under load its resistance rises by 0.5936 Ω. Find the strain ε in microstrain (µε).

R = 350 ΩGF = 2.12ΔR = 0.5936 Ω

ε = µε

6.Hard

A bridge with 1000 Ω arms is excited with 5 V and has one active gauge (quarter bridge). The gauge factor is 2.05 and the strain is 600 µε. Find the bridge output V_o in mV.

V_s = 5 VGF = 2.05ε = 600 µε

V_o = mV

Answer key

1. R₄ = 640 Ω
2. R_x = 23.33 Ω
3. I_g = −26831 µA
4. R_th = 145.5 Ω
5. ε = 800 µε
6. V_o = 1.537 mV

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