ELEC 105 Laboratory Exercise #2 Spring 2010ELEC 105 Laboratory Exercise #2 Spring 2010Basic Circuit Analysis, and Pots for LagniappeWhy is this important?The application of the basic circuit laws such as Ohm’s law, KVL, and KCL are fundamental to understanding how electrical and electronic circuits work and what their limitations and capabilities are. Establishing the relationship between a physical circuit and its mathematical representation is essential to quantifying its operating parameters. This week’s exercise will allow you to practice basic circuit analysis in an environment where you can verify your results by measuring a live circuit. And we’ll throw in something extra: An opportunity to play with a device called a potentiometer, which we will be using in later labs and examples.Lab GradingThis lab is a “familiarization exercise” and therefore will be weighted 50 points. To receive full credit, submit a record of the derivation requested in Step 3 and the two voltage source settings requested in Steps 4 and 6 of the “Circuit Analysis and Measurement” section to your instructor. Only one submissionper lab group is required; however, each member of the group should contribute to its production. The sheet of results is due by 3 pm on the day after your lab session.Circuit Analysis and MeasurementComplete the following tasks as a group. You will need a few sheets of paper or a few pages in a notebook to do analysis and record results and lessons learned. You will be asked to submit a few calculations and results. Please be ready to copy the final forms of your derivations and answers onto a clean sheet of paper. Your submission does not have to be word-processed, but it should be neat enough to be easy to read. 1. Consider the circuit shown in Figure 1. Using Ohm’s law, KVL, KCL, and the definitions of series and parallel elements, find the unknown voltages v1, v2, and v3 and currents i1, i2, and i3 for the case when Va = 5 V and Vb = 15 V. You might want to solve the problem symbolically, since later you will need to derive an expression for v2 in terms of the resistor values and the two voltage source settings.Figure 1. Schematic diagram of circuit to be analyzed and measured.1VaR21 kR1100 i3i2i1R3 = 220 Vb+−+−+v1−+v2−+ v3 −2. You will now verify the voltages and two of the currents you calculated in the previous step. Build the circuit shown in Figure 1 onto your protoboard, using the 0-6 V section of the bench-top power supply for voltage Va and the 0 to +25 V section (or perhaps the 0 to –25 V section) for Vb. Set Va = 5 V and Vb = 15 V. Remember that a link to a resistor color code chart is available on the “Laboratory” page of the course web site. For most of the resistors we have in stock, you will need touse the 4-band code; that is, you should ignore the “3rd Band” column of the color code table. You might want to measure each resistor with the DMM (digital multi-meter) to verify its value. Show your instructor that the voltages v1, v2, and v3 are close to the values you predicted. The power supply display should also indicate close to the correct values of i1 and i3. (The power supply current read-outs do not seem to be very accurate.)3. Derive a symbolic expression for v2 in terms of R1, R2, R3, Va, and Vb. Once you are confident that the derivation is correct, copy it to the clean sheet of paper that you will turn in after the lab session. Using the expression you have derived (or an earlier intermediate step), find the value to which Vb should be set in order to make v2 = 5 V. The values of R1, R2, R3, and Va should remain unchanged. It is possible that the required value of Vb is negative.4. Adjust the ±0-25 V power supply to the new value of Vb that you calculated in the previous step, and verify by measurement that v2 is in fact now 5 V. Record the value of Vb that causes v2 to be 5 V.5. Use your symbolic expression for v2 to find the value to which Vb should be set in order to make v2 = 0 V. The values of R1, R2, R3, and Va should again remain unchanged, and it is again possible that the required value of Vb is negative.6. Adjust the ±0-25 V power supply to the new value of Vb that you calculated in the previous step, and verify by measurement that v2 is in fact now 0 V. Record the value of Vb that causes v2 to be 0 V.Potentiometers1. It is often useful to have a resistor whose value can be changed manually. One type of variable resistor is called a potentiometer, and its circuit symbol is shown in Figure 2. Example applications of variable resistors are volume controls and electronic angular position (direction) sensors. A potentiometer consists of a fixed resistor with a movable “tap,” or connection point, that is wired to a third terminal (labeled “2” in Figure 2). The tap is also sometimes called a “wiper arm.” The resistance between terminals 1 and 2 plus the resistance between terminals 2 and 3 add up to the overall fixed resistance value Rpot. For example, if the tap is 1/4 of the way from one end of a 10-k potentiometer, then an ohmmeter would display 2.5 k between terminals 1 and 2 and 7.5 k betweenterminals 2 and 3. The tap position can be controlled by a wide variety of mechanical means, but the most common is via a rotary shaft. Less common, but still familiar to many people, is a slider that moves along a straight track. Audio mixing boards often use the latter type of potentiometer.Figure 2. Circuit symbol for potentiometer. The circles indicate connection terminals. The numerical labels shown here are not standard; the terminals are not always marked on commercially available potentiometers.2Rpot1232. Obtain a potentiometer from the instructor, and place it on the protoboard. Connect the leads from the DMM to the two outside terminals of potentiometer. What value do you measure, and how does itcompare to the labeled value? When you turn the knob, does the measured resistance between the two outside terminals change significantly (i.e., more than a fraction of a %)? Record the measured resistance on the sheet you will submit to the instructor.3. Now connect the leads from the DMM between the middle terminal (the “tap”) and one of the outsideterminals. Turn the knob back and forth over its full range of motion and observe how the resistance changes. Set the knob anywhere partway through its range and record the