Instrumentation

INSTRUMENTATION

Question 1:

Refer to Figure Q1 below. Two strain gauges are applied to measure the force applied on the steel

bar shown in Figure Q1. All resistance of resistors R3, R4 and the unstressed strain gauges R1 and R2

are 120 Ω. Poisson’s ratio is 0.5. The steel bar has a diameter of 40 mm and the Young modulus of

the steel bar is 9.37 x 1010 N/m2.

a. Determine the output voltage VOUT of the bridge when a load of 50 kN is applied?

b. Determine the sensitivity of the measurement?

c. Determine the output voltage VOUT when the strain gauge R1 is damaged such that R1 is short-

circuited?

d. Determine the output voltage VOUT when the strain gauge R1 is damaged such that R1 is open

circuit?

Question 2:

A Platinum resistance sensor (RTD) has a resistance of 100 Ω at ambient temperature of 00 C and a

temperature coefficient of resistance α = 4 x 10-3 Ω / 0C. This RTD is incorporated at position R1 in

the wheat stone bridge set up in Figure Q2. The ratio of resistance 100

a. Determine the value of resistance R4 such that the output voltage VOUT is 0 Volt when

ambient temperature is 00 C.

b. Determine the required supply voltage V1 such that the output voltage VOUT=100 mV when

ambient temperature T=1000 C?

c. Determine the measurement sensitivity?

Question 3:

The figure Q3 below show a diagram of wheat-stone bridge with two fixed resistors on the left

branch and two temperature sensors (temperature dependant resistors/RTD) on the right branch,

RTherm1 and RTherm2. Their resistances in Ohms are given as function of temperature T in degree

Celsius (0C) as stated here:

RTherm1 = R1 (1+α1T) with α1 = 0.01/ 0C and R1 = 2 kΩ

RTherm2 = R2 (1+α2T) with α2 = - 0.02/ 0C and R2 = 1 kΩ

a. Derive the output voltage VO as a function of temperature T, meaning determine the output

voltage VO = f(T).

b. At which temperature is the bridge balanced?

c. Determine the output voltage VO when T= -100 C and when T= 250 C.

d. Determine the sensitivity of measurement?

e. Assume T=1000 C, what will be VO? Define the feasible range and span of temperatures that can

be measured by this circuit?

Question 4:

A strain gauge with a gauge factor GF=2, is mounted on a rectangular steel bar (with Young modulus

E= 200 x 106 kN/m2) as shown in Figure Q4a below. The steel bar is 3 cm wide and 1 cm high and it

is subjected to a tensile Force of F=30 kN. It is a symmetrical bridge.

a. Determine the resistance change of the strain gauge if the unstressed resistance (no axial load) is

120 Ω.

b. Suggest how can the output voltage EO can be increased by factor 2 and even factor 4 with

additional strain gauges of the same specifications. Determine EO with 1, 2 or 4 strain gauges. Draw

how the strain gauges are being placed on the steel bar and how each strain gauge on the steel bar

is connected to various resistor position in the wheat stone bridge

c. To bring the bridge output voltage to the required voltage range, an instrumentation amplifier is

being applied (see Figure Q4b). State the advantage of using this IA in this application.