Resistance, Current, and Voltage

Transcription

1 Resistance, Current, and Voltage Bob Somers 3/7/05 Per. 4 Phil Jenkins, Katherine Kruser Purpose The purpose of this lab was to apply the concepts of constant voltage and current in parallel and series circuits to establish the fact that our book-learned knowledge actually works in the real world. Calculating the predicted values and then measuring the real values allows us to compare our calculated results with those really present in the circuit. Theory There were a whole lot of concepts behind this lab, which allowed us to compute and observe the results that we did. It was absolutely vital that we knew our voltage and current rules, otherwise constructing the correct circuits would have been a very daunting task indeed. The first challenge was figuring out how exactly to design the circuit. We needed to create a complex circuit with a series chunk and a parallel chunk. There were a couple of possible ways to wire it, but my group chose to wire a parallel circuit within a series circuit.

2 The most difficult part of the lab was making sure that the voltmeter and ammeter were wired into the circuit correctly, so that they would not disturb the existing current or potential difference. Voltmeters are constructed with huge resistors inside with the intention of being connected in parallel with the part of the circuit you want to measure potential difference across. Their huge resistors prohibits current from flowing through its branch, however since it is in parallel it still receives all of the potential difference that every other branch receives. Ammeters are similar in principle, but not in application. Ammeters are built with literally no resistance to allow current to flow completely freely through them. Because of this, they are intended to be wired in series where current is the same among all objects in the series. You have to be very careful when wiring an ammeter, because if it is in parallel with anything all of the charge will rush through the ammeter (due to its low resistance) and fry its internal components. For our potential difference readings, we started by connecting our voltmeter across the power supply terminals to create a separate parallel branch and read the potential difference on the entire circuit. We then moved the voltmeter appropriately about to measure the other potential differences in the circuit. The ammeter was a little more tricky, but since we double and triple checked our circuitry design before flipping the switch we didn t encounter any problems. Procedure 1. Construct a complex circuit such that there are both a series and a parallel subcircuit within the entire circuit. 2. Connect the voltmeter across the terminals of the power supply and the ammeter in series with the entire circuit. 3. Slowly increase the amount of potential difference until it reaches a desirable number and do not touch the dial ever again. 4. Read your and record to a table the measured values. 5. Now connect the voltmeter in parallel with resistor 1 (s) by connecting across the alligator clips. Leave the ammeter in the same position. Measure and record the potential difference and current. 6. Now repeat this process of moving the voltmeter and ammeter to be in their respective locations relative to the last 2 resistors and the entire parallel combination. Continue measuring and recording potential differences and currents.

3 Data Location Color Code Potential Diff. Current Resistor 1 (s) Green Blue 5.9 V Resistor 2 (p) Orange Orange 1.4 V A Resistor 3 (p) Red Red 1.4 V A Parallel Total n/a 1.4 V Circuit Total n/a 7.5 V Observations The resistors were warm after running a trial. The meters had a tiny bit of bounce in them, meaning that when the voltage knob was adjusted they slightly overshot their mark and quickly settled in. When you don t have a good connection between the wires and resistors, the voltmeter and ammeter bounce and jiggle until you have a solid connection. Calculations First we calculate the resistance of resistor 1 (s) using the measured voltage and current. R = 5.9 V R = 54 Ω Next, we calculate the resistance of resistor 2 (p) using the measured voltage and current. R = 1.4 V A R = 35 Ω Next, we calculate the resistance of resistor 3 (p) using the measured voltage and current. R = 1.4 V A R = 23 Ω Next, we calculate the resistance of the total in parallel using the measured voltage and current.

4 R = 1.4 V R = 13 Ω Next, we calculate the resistance of the entire circuit using the measured voltage and current. R = 7.5 V R = 68 Ω Now we calculate the percent error to be analyzed in the following section. (experimental theoretical) x 100 = percent error theoretical (54 56) x 100 = -3.6% 56 By similar processes we obtain +6.1% for resistor 2, +4.5% for resistor 3, +5.1% for the parallel total, and 1.9% for the entire circuit. Error Analysis As always, there is some factor of human error in this lab. However, in this particular lab, where the science is so exact, human error probably played the largest role in skewing our answers. We were forced to estimate between lines on both the voltmeter and the ammeter and were only able to record a precariously small number of significant digits. Slight reading mistakes on the meters coupled with the large rounding error due to lack of sig-figs probably can account for two-thirds or more of the error. However, there is a small amount of error contributed by a source that most would never think about. The wires themselves were resistors, albeit very small ones. Given that we used, for the most part, wire longer than necessary to run our tests, it is quite possible that a small amount of the error recorded was generated by the minute resistance of these wires. Conclusion Even when the error is factored in, the results are still quite clear: this stuff actually works. It was apparent even when we were actually performing the lab, way before we started calculating anything or pushing numbers around. A lot of the same numbers started showing up, which at the time was both comforting and disturbing. However, after applying a small bit of logic, we were successfully able to determine which readings should match and therefore were able to check ourselves along the way. If something weird or unexpected showed up, we already had the concepts firmly planted into our head that told us we must have done something wrong. I personally enjoyed this lab a lot because it gave us the chance to fiddle with circuits on a large enough scale (as opposed

5 to integrated circuits or likewise) to actually learn and see where the current is flowing. I m already getting excited because half of my Computer Engineering major in college will be Electrical Engineering and this stuff is just plain fun.