The University of Toledo EECS:2300:xx Electric Circuits wheatstone_bridge.fm - 1 Dr. A.D. Johnson

Lab Assignment #4

WHEATSTONE B RIDGE

1. OBJECTIVES - introduction to resistance measurement method which eliminates influence of the values of internal resistances of voltmeters and ampermeters; - increasing the familiarity with the laboratory power supply and digital ; - increasing familiarity with the layout of the protoboard and its application to building experimental physical circuits.

2. P RELAB A SSIGNMENT

2.1 D RAWING THE PHYSICAL LAYOUT OF THE CIRCUIT

Using the template shown in Figure A-5.1, prepare a drawing of the physical layout of the experimental circuit whose electrical model is shown in Figure A-2.1; show the prepared drawing in your Lab report as Figure 2.1. In the prepared drawing, show exact positions of all circuit elements, power sources, and measurement instruments, as well as the points of contact on the protoboard of the wires which will be used to make the interconnections.

R1 R2 A V + S -

R3 RX

Figure A-2.1 The Wheatstone for measurement of the unknown resistance R x.

Hint 1# Make a copy of the protoboard template shown in Figure A-5.1 at the end of this assignment, and prepare the Figures 2.1 using that template.

2.2 FORMULA FOR CALCULATING THE UNKNOWN RESISTANCE VALUE R X WHEN THE IS BALANCED

Applying the divider’s formula, derive the expression for the unknown resistance R x in the balanced bridge. Show the derived formula as equation (2.2-1).

 2001 by Dr. Anthony D. Johnson. All rights reserved. No part of this document may be reproduced, in any form by any means, without permission in writing from the author. The University of Toledo EECS:2300:xx Electric Circuits wheatstone_bridge.fm - 2 Dr. A.D. Johnson

3. L AB EQUIPMENT AND CIRCUIT COMPONENTS

3.1 EQUIPMENT Equipment to be used includes: - Protoboard Global PB-104, - Digital , - DC power supply.

3.2 CIRCUIT COMPONENTS - Connecting wires, - Precision .

4. LAB E XPERIMENT

To measure the unknown resistance R x in the circuit model of Figure A-2.1, the bridge must be balanced by adjusting the value of the resistance R 3 until the ampermeter in the diagonal branch of the bridge shows no current flow. 4.1 MEASURE THE UNKNOWN RESISTANCE VALUE USING THE W HEATSTONE BRIDGE CIRCUIT 4.1.1Using as a reference the drawing of the prepared physical layout, shown in Figure 2.1, build on the protoboard the physical circuit whose electrical model is shown in Figure A2-1.

4.1.2 Adjust the value of the resistance R 3, and read the miliampermeter showing the current IA until it shows negligible current, then enter the value of resistance R 3 into the "R 3" column of Table T-4.1. Table T-4.1

Ω] Rx[ Ω R3 [ ] Wheatstone .

4.2 VERIFY THE UNKNOWN RESISTANCE VALUE USING THE O HMMETER FUNCTION OF THE DIGITAL MULTIMETER

Make the appropriate settings for the Ohmmeter function of the digital multimeter, and measure the value of the R x using the digital multimeter. Enter the measured resistance value into the "Ohmmeter" column of Table T.4-1.

 2001 by Dr. Anthony D. Johnson. All rights reserved. No part of this document may be reproduced, in any form by any means, without permission in writing from the author. The University of Toledo EECS:2300:xx Electric Circuits wheatstone_bridge.fm - 3 Dr. A.D. Johnson

5. P OSTLAB A SSIGNMENT

5.1 CALCULATE THE VALUE OF THE UNKNOWN RESISTANCE R X USING THE KNOWN W HEATSTONE

BRIDGE RESISTANCE R 3 VALUES

Applying the derived formula (2.2-1), to the measured resistance R 3 values from table T-4.1, calculate the corresponding values of resistance R x, and enter the calculated values into the "Wheatstone" column of table T-4.1.

5.2 ASSESSING THE INFLUENCE OF THE MEASUREMENT CIRCUIT ON THE CORRECTNESS OF THE RESULT

Compare the calculated values of the resistance R x from table T-4.1 with the values measured using the digital Ohmmeter. Make an observation as to the possible discrepancies. Are the values in one of the columns systematically smaller/greater than those in the other column? How does the precision with which we know the value of the voltage of the voltage source in the Wheatstone bridge circuit influence the correctness of the result of measurement. How does the precision with which we know the values of the known resistors in the Wheatstone bridge circuit influence the correctness of the result of measurement. Hint 2# For the last two questions consult the derived formula (2.2-1).

6. LAB REPORT

To be considered complete, the Lab #4 report must contain the following, 1. Cover sheet - Lab style, filled out, 2. The result of prelab work under 2.1 through 2.2 3. The result of experimental work under 4.1 through 4.2. 4. The result of postlab work under 5.1 through 5.2. 5. A report on items not already included under 2. through 4. above, but listed in the Lab Policies & Procedures, which includes, but may not be limited to the following, - a discussion of the insights gained through the conducted experiments, - description of implemented testing procedures, - comments and suggestions that might lead to an easier and/or deeper understanding of the topics covered by the assignment.

 2001 by Dr. Anthony D. Johnson. All rights reserved. No part of this document may be reproduced, in any form by any means, without permission in writing from the author. The University of Toledo EECS:2300:xx Electric Circuits wheatstone_bridge.fm - 4 Dr. A.D. Johnson

Hint #4 Each group of five adjacent holes aligned alligned in the same direction has access to the same circuit node. Each hole belongs to one group only.

Figure A-5.1 Template showing the layout of the protoboard on which the experimental circuits will be built in the Lab.

 2001 by Dr. Anthony D. Johnson. All rights reserved. No part of this document may be reproduced, in any form by any means, without permission in writing from the author.