Purpose

To experimentally test the behavior of a Wheatstone Bridge circuit.

To use a potentiometer as a variable resistance analog.

To experimentally investigate how to make very precise resistance measurements.

Prelab

1. Read the lab exercise and familiarize yourself with the procedure.

2. Familiarize yourself with the basics of a Wheatstone Bridge circuit using texts, course notes, or internet sources.

3. Print this datasheet and bring it with you to the lab.

Theory

A Wheatstone bridge allows for the determination of an unknown resistance by means of a balancing circuit. The balancing circuit, by way of a variable resistance, allows the investigator to alter the current flow in a measurement path to zero (or near zero in practice). Since current measurements can be made in the pA range (much, much lower inherent error than resistance measurements) a precise value for the resistance of an unknown component can be determined. Further, the circuit can indicate any variance from the "zero'ed" value by way of the increased current flow in the current measuring device.

Problem

AP Engineering Inc. designs instrumentation used by civil engineers to detect faults and disturbances in infrastructure that may indicate potential failure or unsafe conditions. GM Contracting has recently finished work on a concrete bridge that spans a local waterway and has hired AP Engineering to install instrumentation to monitor the bridge. The instrumentation, in simple terms, behaves as follows:

A Wheatstone bridge is designed and installed such that a flexible & elastic resistor embedded in the concrete of the bridge acts as R_x as shown in the circuit diagram below. Any displacement or movement of the structure that causes a change in the position or shape of the concrete will cause a change in the resistance value of the embedded resistor. The initial value of this resistor is not precisely known. If the resistance changes beyond a certain amount (high or low) an alarm or alert will sound to the relevant city personnel in charge of safety.

GM Contracting has provided the following data for consideration:

• On the day of installation it is desired for the alarm to read a "zero" for the measured displacement of the bridge to indicate that it is standing as designed.

• The alert should trigger if the embedded resistor indicates ±4.2cm from initial conditions where the resistor changes value by 100Ω/cm.

  • eg: a deflection of +1.2cm would result in a change of 120 Ω. If the initial value were 2.70 kΩ, the embedded resistor is now 2.82 kΩ.

At time of installation a junior engineer is tasked with the following:

• Determine the initial setting for the potentiometer to "zero" the alarm and show no movement has occurred in the structure.

• Determine the upper and lower resistance & accompanying current values that indicate crossing of the unsafe threshold for bridge safety.

Results

• Compare the theoretical (via multisim) and measured value of R₂ given that R_x is precisely 6.81 kΩ.

• What then must the value of the embedded resistor R_x have been at the time of installation? Show your work.

• As required by the problem statement, what current values (as continuously measured by the instrument) would set off the alarm?

Questions

1. Under the condition that no current flows from A to B what can be said about:

   • The current i₁, i₂, i₃, & i_4/x?

   • The voltage at node A and Node B?

2. What factor in the measurement setup is the greatest source of error in terms of the deviation caused from theoretical?