1/4 University of Rochester Department of Electrical & Computer Engineering ECE111 Laboratory #1 Simple DC circuits week of 14 Sept, 09 --------------------------------------------------------------------------------------------- Unless prior arrangements are made with the instructor, all laboratories are to be conducted during regularly scheduled lab sessions in Gavett 306. Students are expected to work in teams of two. Data, circuit setups, component values, and relevant calculations must be recorded in a spiral notebook with each page numbered and dated. Before leaving the lab, get your TA to sign and date each page. Lab write-ups (one per team of two students) are due at Hopeman 304 by 1700 hrs one week after the laboratory has been performed. Late work will not be accepted. Write-ups must be prepared with word-processing software and should be organized as follows: 1) statement of laboratory objectives; 2) concise description of lab procedures with diagrams of all circuits; 3) detailed description of the results with error and precision; 4) discussion and conclusions; 5) on a separate sheet - stapled to the top of the report - prepare an abstract as described in the website. Report grades will be based upon conciseness, grammar, and spelling, as well as completeness and correctness of quantitative results. Poorly written reports will be returned for revision. --------------------------------------------------------------------------------------------- 0. Laboratory preparation Prepare for this lab by reviewing voltage & current divider network relations as covered in lectures and in the text. Do not forget to obtain a proto board from the electronics shop on the 2nd floor of Hopeman before coming to the lab. Also, bring a spiral notebook (one per lab team) to record your lab data. You will not be allowed to start the lab without this notebook. In this and subsequent lab assignments, you will be collecting resistors and other components from the marked drawers to build your circuits. Unless stated otherwise, you should simply select the components you need, measure their values using the RLC bridge found at the front of the lab room, and then record them on your lab book. It will almost never be necessary to use better than standard ±10% components, so do not waste time looking for “perfect” resistor values. In this lab, you will investigate KCL and Vbat 10 kΩ + - v2 5 kΩ 2 kΩ 100 Ω v1 + - + i A Fig. 1. Parallel resistive circuit for KCL test.-2- KVL, i.e., Kirchhoff’s current and voltage laws for resistive circuits with a 9 Volt battery as the voltage source. I. Current divider Build the circuit shown in Fig. 1 and then use an oscilloscope to measure the voltage drops necessary to calculate values of the currents flowing through all the resistors. Be sure to take into account the uncertainties of the resistors and errors on measurement. Use your results for these current values to check the condition enforced by KCL at node A, which is marked by an arrow in the figure. In your lab write-up, make sure to write down an expression for KCL in the form specific for this circuit. As part of this exercise, you also should estimate measurement errors due to the scope and use this information as you compare the calculated and measured values. Do not use too many places of accuracy in your answer. II. Voltage divider Build the circuit shown in Fig. 2 and then use the oscilloscope to measure the voltages across the three individual series resistors. After recording these voltage values, use them to check the validity of KVL for the circuit loop, taking into account the uncertainty of the resistor and battery voltage values. In your lab write-up, make sure to write down KVL in the form specific for this circuit. As before, please make sure to estimate the uncertainties of all numerical values, both calculated and measured. III. Current measurement Next, build the circuit shown in Fig. 3, using some resistor Rx in the range from 5 kΩ to 20 kΩ. Measure only the total battery voltage Vbat and the voltage vc across the 100 Ω resistor. Calculate the current i = vc/100 and use this current value to calculate the quotient: Vbat/i. Compare your result to the value of your resistor Rx, as independently obtained using the RLC bridge. These values should be rather close, but probably not identical. Vbat 5 kΩ + - 2 kΩ 1 kΩ i Fig. 2. Resistive voltage divider circuit for testing KVL.-3- After you have completed this exercise, ask the TA to give you another (unknown) resistor Rx. Repeat the procedure to obtain a value for the unknown and its uncertainty in ±%. When you think you know what the value is, ask the TA for the true value. If you are in error, go back and try to find where you went wrong. This method of using a small current detection resistor is a very common and useful technique for measuring voltage and current in unknown components. Note that it is only accurate if Rc << Rx. In the write-up, explain why this is so. IV. Wheatstone bridge Build the Wheatstone bridge circuit shown in Fig. 4, using a 20 kΩ potentiometer for one side of the bridge and two resistors, R1 = 5 kΩ and R2 = 10 kΩ on the other side. Set up the oscilloscope to measure the voltage difference vg. (In the classical Wheatstone bridge, vg was usually monitored by a galvanometer. Here, an oscilloscope serves as a very sensitive and adequate substitute.) Once your circuit is working, you should see a DC voltage vg that may be positive or negative. By turning the potentiometer, this voltage will rise or fall. Adjust the “pot” until you get zero. This is the condition where the two resistive dividers are exactly balanced. When you have obtained this condition, carefully remove the pot from the circuit and measure the two resistance Ra and Rb. Compare the two resistive ratios: Ra/Rb and R1/R2. Within the limits of precision, they should be equal. Vbat RX + - vc RC = 100 Ω + i Fig. 3. Current measuring circuit for measuring