ALUND Lab 4 Compound Circuits

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Electrical Engineering

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Feb 20, 2024

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PHY 112 L Lab 4: Compound Circuits 1. Testable Question: Part A. How is the current affected by the voltage in a circuit? 2. Hypothesis: Part A. If the voltage increased than the current will increase because the voltage is moving the electrons faster through the current. 3. Variables: Work with your team. List and identify the different variables used in the experiment. Be sure to include each variable’s symbol in parentheses. Control(s): resistance (R) Independent: Current (I) Dependent: Voltage (V) 4. Experimental Design: i R ( Ω ) V (v) I (A) 1 – 5 R1 V 1-5 I 1-5 1 – 5 R2 V 1-5 I 1-5 1 – 5 R3 V 1-5 I 1-5 1 – 5 R4 V 1-5 I 1-5 1 – 5 R5 V 1-5 I 1-5 5. Materials:  DC power supply  Ammeter  Resistors (5)  Circuit wires  Alligator clips 6. Procedures: 1. Obtain 5 different resistors

PHY 112 L 2. For each resisir, use the colored diagram provided by the professor and record the values obtained as the calulayted resistance. Repeat for each resistor 3. Measure the resistance of each resitor using the volmeter and record as the measured resistance. 4. For the next portion, there will be five incrimits of 2 (2, 4, 6, 8, 10) which the DC power supply will be at. 5. Putting the DC supply to 2 volts, measure the voltage through each resitor and record in measures voltage. Do this for each resitor at 2V, 4V, 6V, 8V, and 10V 6. After the voltages have been obtained, the same procedure will be performed but to find the current through the resitors. 7. Repeat the same intervals for each resitor. For the compound circuit: 1. Draw your circuit diagram (schematic). Label all the resistors and power supply voltage values. You can either make it from scratch, in Paint or draw it out on white paper or on a white board and then photograph it. Include that as your Setup figure for the Procedures. 2. Draw your circuit diagram again, but this time include ammeters and voltmeters everywhere you plan to measure current and voltage, respectively. Include this before the steps in the procedure for which the placement of the ammeter and voltmeter are described. Do not include the values of the power supply voltage and resistances, just include the symbols for these (include subscripts on the resistors). 3. Use the DMM as an ohmmeter to measure all the resistances before connecting the circuit and then, for the entire circuit before hooking up the power supply. Alternatively, you can use the results of the Ohm’s law measurements to achieve a precise value for the resistance of each resistor.

PHY 112 L 7. Data Table: Table 1: Resistors resistor bands calculate (ohms) measured (ohms) % error R1 orange-orange brown 330 334 1.21 R2 red-red brown 220 244 10.9 R3 orange-black brown 300 326 8.67 R4 green-blue brown 560 618 10.4 R5 red-purple brown 270 262 2.96 Table 2: Ohms Law Experiment - Resistor 1 OO B DC supply voltage (v) measure s voltage (V) calculated current (A) measured current (A) error (of current) % error (of current) measured (mA) 1.99 1.97 0.00590 0.00590 0.0003 0.030 5.90 3.00 2.99 0.00895 0.00880 0.0170 1.699 8.80 4.00 3.96 0.01186 0.01180 0.0047 0.475 11.80 5.00 4.98 0.01491 0.01470 0.0141 1.410 14.70 6.00 5.97 0.01787 0.01780 0.0042 0.415 17.80 Table 3: Ohms Law Experiment - Resistor 2

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PHY 112 L DC supply voltage (v) measure s voltage (V) calculated current (A) measured current (A) error (of current) RR B 1.99 1.98 0.00811 0.00800 0.0141 1.414 8.00 3.00 2.96 0.01213 0.01210 0.0026 0.257 12.10 4.00 3.97 0.01627 0.01610 0.0105 1.048 16.10 5.00 4.96 0.02033 0.02010 0.0112 1.121 20.10 6.00 5.97 0.02447 0.02410 0.0150 1.501 24.10 Table 4: Ohms Law Experiment - Resistor 3 OBLACK B DC supply voltag e (v) measure s voltage (V) calculated current (A) measure d current (A) error (of current) 1.99 1.98 0.0061 0.00600 0.0121 1.212 6.00 3.00 2.98 0.0091 0.00900 0.0154 1.544 9.00 4.00 3.98 0.0122 0.01210 0.0089 0.889 12.10 5.00 4.97 0.0152 0.01520 0.0030 0.298 15.20 6.00 5.98 0.0183 0.01820 0.0078 0.783 18.20 Table 5: Ohms Law Experiment - Resistor 4 GB P DC supply voltage (v) measure s voltage (V) calculated current (A) measured current (A) error (of current) 1.99 1.98 0.0032 0.00330 0.0300 3.00 3.30 3.00 2.99 0.0048 0.00490 0.0128 1.28 4.90 4.00 3.98 0.0064 0.00660 0.0248 2.48 6.60 5.00 4.98 0.0081 0.00830 0.0300 3.00 8.30 6.00 5.98 0.0097 0.01000 0.0334 3.34 10.00 Table 6: Ohms Law Experiment - Resistor 5 RPB DC supply voltage (v) measure s voltage (V) calculated current (A) measured current (A) error (of current) 1.99 1.97 0.0075 0.00750 0.0025 0.254 7.50 3.00 2.98 0.0114 0.01130 0.0065 0.651 11.30 4.00 3.96 0.0151 0.01510 0.0010 0.096 15.10 5.00 4.97 0.0190 0.01880 0.0089 0.893 18.80 6.00 5.98 0.0228 0.02260 0.0098 0.983 22.60

PHY 112 L Table 7: Compound Circuit Table: Measured Measured Measured Measured Calculated Calculated % error % error i R i ( Ω ) V i (V) I i (mA) I (A) V i (V) I i (A) Voltage Current R eq 454 9 41.9 0.0419 0.0199 N/A 1 334 6.60 19.6 0.0196 6.5464 0.0198 0.819 0.812 2 244 2.38 9.7 0.0097 2.3668 0.00975 0.558 0.555 3 326 2.38 7.2 0.0072 2.3472 0.00730 1.397 1.378 4 618 1.68 2.7 0.0027 1.6686 0.00272 0.683 0.679 5 262 0.70 2.7 0.0027 0.7074 0.00267 1.046 1.057 *did not measure/record overall circuit’s velocity or current **calculated data is based off the 9V that was put though the circuit when taking measurements for each resistor . Calculated R eq = __454 Ω ___ % error = ____0.44%______ 8. Analysis: 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 0.00000 0.00500 0.01000 0.01500 0.02000 0.02500 0.03000 f(x) = 0 x + 0 R² = 1 f(x) = 0 x − 0 R² = 1 f(x) = 0 x − 0 R² = 1 f(x) = 0 x + 0 R² = 1 f(x) = 0 x − 0 R² = 1 I vs V orange-orange brown Linear (orange-orange brown) red-red brown Linear (red-red brown) orange-black brown Linear (orange-black brown) green-blue brown Linear (green-blue brown) red-purple brown Linear (red-purple brown) Linear (red-purple brown) V (V) I (A) Ohm’s Law Experiment: Resistor 1: TS: R 1 TS: 330Ω MS: 334Ω

PHY 112 L % error = | 330 Ω − 334 Ω | 330 Ω × 100 % error = 1.21% Resistor 2: TS: R 2 TS: 220Ω MS: 244Ω % error = | 220 Ω − 244 Ω | 220 Ω × 100 % error = 10.9% Resistor 3: TS: R 3 TS: 300Ω MS: 326Ω % error = | 300 Ω − 326 Ω | 300 Ω × 100 % error = 8.67% Resistor 4: TS: R 4 TS: 560Ω MS: 618Ω % error = | 560 Ω − 618 Ω | 560 Ω × 100 % error = 10.4% Resistor 5: TS: R 5 TS: 270Ω MS: 262Ω % error = | 270 Ω − 262 Ω | 270 Ω × 100 % error = 2.96% Compound Circuit Analysis: R 45 : R 45 = R 4 + R 5 R 45 = 618Ω + 262Ω R 45 = 880Ω R 2345 :

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PHY 112 L R 2345 = ( 1 R 2 + 1 R 3 + 1 R 45 ) -1 R 2345 = ( 1 244 Ω + 1 326 Ω + 1 880 Ω ) -1 R 2345 =120.45 Ω R eq : R eq = R 1 + R 2345 R eq = 334 Ω + 120.45 Ω R eq = 454.45 Ω I 1 : I 1 = V 1 /R 1 I 1 = 6.60V/334 Ω I 1 = 0.0198 A I 2 : I 2 = V 2 /R 2 I 2 = 2.38V/244 Ω I 2 = 0.00975 A I 3 : I 3 = V 3 /R 3 I 3 = 2.38V/326 Ω I 3 = 0.00730 A I 4 : I 4 = V 4 /R 4 I 4 = 1.68V/618 Ω I 4 = 0.00272 A I 5 : I 5 = V 5 /R 5 I 5 = 0.70V/262 Ω I 5 = 0.00267 A I tot : I tot = V tot /R eq I tot = 9V/454 Ω I tot = 0.0198 **voltage used was the total voltage read from the voltmeter as the voltage through the entire circuit was not recorded. V 1 : V 1 = R 1 *I 1 V 1 = 334 Ω*0.0198A V 1 = 6.55 V V 2 : V 2 = R 2 *I 2

PHY 112 L V 2 = 244Ω*0.00975A V 2 = 2.37 V V 3 : V 3 = R 3 *I 3 V 3 = 326Ω*0.00730A V 3 = 2.35 V V 4 : V 4 = R 4 *I 4 V 4 = 618Ω*0.00272A V 4 = 1.67 V V 5: V 5 =R 5 *I 5 V 5 = 262Ω*0.00267A V 5 = 0.707 V 9. Conclusion: (Ohm’s Law Experiment, only) The current is directly linear and proportional to that of the voltage according to the following equations obtained from the graph: R1) I = (0.003A/v)V - 1.0*10 -5 A R2) I = (0.004A/v)V + 1.0*10 -4 A R3) I = (0.0031A/v)V - 8.0*10 -5 A R4) I = (0.0017A/v)V - 8.0*10 -5 A R5) I = (0.0038A/v)V + 0.0001A 10. Evaluation: The hypothesis was supported that as the voltage increased, the current also increased linearly. The accuracy of the results ranged from excellent to fair with the lowest percent error being 1.21% and the highest being 10.9%. For resisters 1-4, the TS value was smaller than the MS value while resistor 5 had a higher TS value than the MS value. A possible source of systematic error could come from loose connections with the wires as well as some resistors having more oxidation on them than others. For all five of the resistors within this experiment, the precision was outstanding based on the R 2 values of resistor one of 0.997 and the following four of 0.999. A source of random error could come from human error in reading the values presented by the voltmeter. The numbers fluctuate and the person reading the numbers took the higher number that was shown. In the compound circuit portion, the main error was that of human error in the fact that the overall current, and resistance of the entire circuit was not recorded. The values within the table were based on the voltage going through the circuit that the voltmeter was set to.

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