FE Other Disciplines Instrumentation and Controls Practice Problems

The current FE Other Disciplines specification assigns 4-6 of the 110 exam questions to Instrumentation and Controls. Form A contains 5 original problems in this area. The sample below is published in full, with the same worked-solution format used throughout the book.

A single active foil strain gauge occupies one arm of a Wheatstone bridge; the other three arms are fixed resistors of the same nominal resistance. Bridge excitation is $10.0$ V DC, the gauge factor is $2.10$ , and the bridge output drives an instrumentation amplifier of gain $250$ . For a surface strain of $850 \times 1 0^{- 6}$ m/m, the amplifier output voltage is most nearly:

(A)0.253 V
(B)1.12 V
(C)2.23 V
(D)4.46 V

Show worked solution

Answer: (B)

Only one bridge arm is active, so the bridge delivers 4.46 mV and the gain-250 stage raises it to about 1.12 V.

A quarter bridge converts the fractional resistance change of its one active arm into a differential output equal to a quarter of the excitation times that fraction.

\frac{Δ R}{R} = GF \cdot ε = 2.10 (850 \times 1 0^{- 6}) = 1.785 \times 1 0^{- 3}

V_{o} = \frac{V _{e x}}{4} \cdot \frac{Δ R}{R} = \frac{10.0}{4} (1.785 \times 1 0^{- 3}) = 4.4625 \times 1 0^{- 3} V

Gain of the signal-conditioning stage lifts this millivolt-level difference to a range a data acquisition input can resolve.

V_{o u t} = 250 (4.4625 \times 1 0^{- 3}) = 1.12 V

FE Reference Handbook — Instrumentation, Measurement, and Controls: Wheatstone Bridge and Strain Gauge Relations

Why the other choices appear

(A)Dividing the strain by the gauge factor instead of multiplying: $(10.0/4) (850 \times 1 0^{- 6} /2.10) (250) = 0.253$ V.
(C)Using the half-bridge sensitivity $V_{e x} /2$ in place of $V_{e x} /4$ , which doubles the result to 2.23 V.
(D)Omitting the factor of 4 altogether: $(10.0) (1.785 \times 1 0^{- 3}) (250) = 4.46$ V.