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 20 Ω resistor sits in the left gap and an unknown resistor Rₓ in the right gap. The galvanometer reads zero when the jockey is 65 cm from the left end A of the 100 cm wire. Find R_x.

R = 20 Ωl = 65 cmL = 100 cm

R_x = Ω

2.Easy

The Wheatstone bridge in the diagram is balanced: the galvanometer reads zero. R₁ = 120 Ω, R₂ = 120 Ω and R₃ = 50 Ω. Find the unknown resistor R₄.

R₁ = 120 ΩR₂ = 120 ΩR₃ = 50 Ω

R₄ = Ω

3.Medium

A 1000 Ω strain gauge is one arm (R₂) of a bridge with four equal 1000 Ω arms and an excitation of 6 V. Find the power P_g dissipated in the gauge, in mW. Self-heating limits the excitation.

V_s = 6 VR = 1000 Ω

P_g = mW

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 = 200 ΩR₂ = 50 ΩR₃ = 40 ΩR₄ = 120 ΩR_g = 200 Ω

I_g = µA

5.Hard

A bridge with 120 Ω arms is excited with 2.5 V and has four active gauges, two in tension and two in compression (full bridge). The gauge factor is 2.12 and the strain is 750 µε. Find the bridge output V_o in mV.

V_s = 2.5 VGF = 2.12ε = 750 µε

V_o = mV

6.Hard

A 120 Ω strain gauge with gauge factor 2.1 is bonded to a steel bar. Under load its resistance rises by 0.126 Ω. Find the strain ε in microstrain (µε).

R = 120 ΩGF = 2.1ΔR = 0.126 Ω

ε = µε

Answer key

1. R_x = 10.77 Ω
2. R₄ = 50 Ω
3. P_g = 9 mW
4. I_g = −12222 µA
5. V_o = 3.975 mV
6. ε = 500 µε

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