Basic Circuit Laws

Week 10: Basic Circuit Laws

Objectives

The Objectives of this lab are to:

• Use Kirchoff’s Voltage Law (KVL) and Kirchoff’s Current Law (KCL) to find the unknown quantities in a circuit.
• Practice using matrices to solve systems of simulataneous linear equations.
• Learn how to create a simple circuit on a breadboard.
• Learn how to properly use a DMM to measure electrical quantities in a circuit.
• Understand basic relationships among voltage, current and resistance in a circuit through measurements.
• Learn the theory of additivity of normal distributed variables.

Pre-laboratory Preparation

In addition to the weekly expectation of a pre-lab for this lab that includes Objectives, Apparatus, Planned Procedure, and outlines of any tables needed for data collection, the following should be completed before class:

Complete the Active Learning Exercise on page 3-4 of the reading material for this week [Week 10 Reading – Electrical Circuits and Basic Circuit Laws] located in Blackboard as part of your pre-lab preparation. Place the results of the exercise from Excel into your logbook.

Laboratory Procedure

1. Examine the circuit shown in Figure 1.    

[pic 1]

Figure 1: Lab Circuit[pic 2]

1. Your instructor will provide five resistors from the group of resistors you used in the previous lab activity and one different resistor to build the circuit in Figure 1.  The dissimilar resistor is R and the five similar resistors are in the two parallel legs.

1. Your instructor will identify what voltage will be used for Vs.

1. Using KVL and KCL develop 3 equations. Use Ohm’s law and passive sign convention to express all the equations in terms of R and I only.

1. Organize the equations in proper order and express in Matrix form.

1. Using the matrix function in Excel, solve the system of equations for each current (I) identified in Figure 1. Compute voltage drop in each resistor. Prepare a formatted table with nominal resistance, computed current, and computed voltage.

1. Using your knowledge of combining resistances in series and parallel, find equivalent resistance (Req) of the circuit.

1. Build the circuit using a breadboard and resistors.  Measure Req and compare with the calculated value.  If the two are close in value, show your circuit to instructor and connect the power supply provided.  Set the power supply value, Vs, to the value given by your instructor.

1. Measure the value of resistance, current, and voltage drop at each resistor.  Report the measured values in the above table alongside the computed values.

1. Calculate the percent error between the calculated and the measured values.

1. Using the measured value of resistance and the measured value of the current, compute the power consumption and corresponding uncertainty at each resistor.

1. Using the power consumption in each resistor, compute the total power consumption in the circuit and the corresponding uncertainty.

1. Use the whole class data from last week and theory of additivity of normally distributed variables to find the normal distribution parameters for Rleg1 and Rleg2.  Measure Rleg1 and Rleg2.

1. Determine whether the measured resistances are within 1, 2, or 3 standard deviation of the mean, i.e., determine the integer M for each case:

[pic 3]

[pic 4]

Deliverables

Write a formal technical report that describes your measurement and analysis results. Be sure to discuss %difference between computed and measured quantities. Is the magnitude of differences similar for current and voltage? Your formal report should include properly formatted tables and graphs derived from your Excel spreadsheet and hand calculations, as appropriate, to present your results. Be sure to answer all questions and make all calculations required. Sample calculations should be included in the Appendix of the report.