Series and Parallel Circuits Lab Report

Experiment 4: Series and Parallel Circuits Abstract The objective of this experiment is to understand the difference of series and parallel circuits, and how they can be combined to make complex circuits. Additionally, this experiment gives an understanding on how to calculate the equivalent resistance and applying Ohm’s Law. This is tested be determining the resistances of four circuits by measuring the voltage and current of the constructed circuits. Also, by observing the behavior of the light bulb’s connection to the series and parallel helps gain an understanding on the strengths and weakness of both types of circuits. The percent error within the experiment is low as majority of the readings were done through a machine, this eliminates most human errors of reaction time and misreading. Applications of this experiment range from basic understanding of engineering and physics such as computer engineers and physicists, all the way to basic electrical set up. This is important as it helps make an efficient electric circuit when making basic machines. Introduction Calculating Equivalent Resistance A resistor means a device that obeys Ohm’s Law and has a resistance R. Ohm' s Law :V = IR Equation 1 Where V is voltage measured in volts, I represents current which is measured in amperes, and finally R or Ω describes resistance which is measured in Ohms. Resistances can be connected in two different forms, series and parallel circuits. These resistors can also be combined to form a complex circuit, a circuit which includes a mixture of both series and parallel. Figure 1: Resistors in series For a series circuit, the resistances are additive, where Req is the equivalent resistance. Req =R1 + R2 Equation 2 For a parallel circuit, the resistance adds as reciprocals 1 1 1 = + R eq R1 R2 Equation 3 If we take both reciprocal of both sides, we end up with the expression Req = R1 R 2 R 1+ R 1 Equation 4 Figure 3: Resistors in parallel For complex circuits, combine all parallel portions with Equation 4 to create smaller series and from their combine all the series portions with Equation 2. Power Power is the rate at which work is done for a system, and electrical power is defined as: P=IV Equation 5 P is defined as power and is measured in watts; this equation is important as it can be derived if the voltage is unknown to get the following equation. P=IV = I ( IR )=I R 2 Equation 6 This shows that power is directly proportional to resistance and the current squared. Therefore, if there are two different circuits, device 1 and device 2, and they both shared the same resistance, but device had double the current. Then device 1 would have 4 times as much power versus device 2. Apparatus The following experiment requires the following: 1 AC/DC Electronics Laboratory EM-8656, 1 Set of circuit components, 1 Digital Storage Oscilloscope TBS 4-1052, 2 Oscilloscope Probes, 1 Digital Multimeter EX 330, and 1 DC Power Supply TP3005T. Figure 4: The digital multimeter used in the experiment which is inserted in series with the power supply to determine the current provided by the source. The “A” symbol refers to ammeter, which is the DMM in current sensing mode. The experiment also requires 4 different lightbulb circuits: Additionally, the experiment needs four circuit diagrams: Figure 9: Circuit diagrams used throughout the experiment Procedure Procedure A: Series and Parallel Resistors Circuits First start by constructing the first circuit shown in the Diagram 1 (Fig 9), and as shown in Figure 4, insert the digital multimeter in series with the DC power supply. This will measure the current provided to the entire circuit by the power supply. Set the DMM to be on the milliampere scale by turning the dial to “mA” (DO NOT connect the power supply to the circuit). Turn on the DC power supply and verify both voltage and current are set to zero by pressing the knob of each and setting the Volts and Amps to 0.000 volts and amps respectfully. Now the power supply can be connected to the circuit and set the voltage to 15.00 V. Slowly increase the current in increments of 0.010 A until 15.00 V has been reached on the power supply. From here record the current being measure by the DMM in Table 2, and then set the current to 0.000 A on the DC power supply. Calculate the theoretical equivalent resistance Req for the circuit by using equations 2 and 3 and enter these values in Table 2. Procedure B: Series and Parallel Lightbulb Circuits Similarly, to the previous section, here the measurement of each lightbulb’s resistance will be measured. From there they will be constructed into series or parallel combinations and measure the equivalent resistance of these combinations. Ohm’s Law states that the resistance of the lightbulb is not constant. Connect lightbulb A in series directly to the power supply, as shown in Figure 5, and turn on the DC power supply. The current and voltage should be zero from the previous experiment. Set the voltage to 2.00 V, and slowly increase the current in increments of 0.010 A (10 mA) to reach the 2.00 V. This should be about 0.260 A for the specific lightbulbs being used. Calculate the resistance of bulb A with these parameters, using, using the voltage and current as displayed by the power supply. Record the value in Table 3 below. Make sure the current is set to zero. Place bulbs A & B in series as shown in Figure 6, 7, and 8. Data Table 1: Measured Resistor Values R1 = 330 Ω 331 Ω R2 = 560 Ω 556 Ω R3 = 100 Ω 99 Ω R4 = 100 Ω 99.2 Ω R5 = 560 Ω R6 = 330 Ω 553 Ω Figure 10: Actual resistance values of each resistors used in the experiment 326.3 Ω Table 2: Resistance Values Circuit Diagram Theoretical Req (Ω) Measured Current (mA) Measured Req (Ω) Percent Difference (%) 1 890 16.78 893.9 0.437 2 207.6 68.8 218.0 4.887 3 307.6 47.4 316.5 2.852 4 383.3 38.43 390.3 1.817 Figure 11: Comparison between the theoretical Req and the measured Req for each circuit diagram Table 3. Lightbulb circuit resistance values Bulb System Measured Resistance (Ω) A 6.4 B 6.7 C 6.5 A&B Series 8.6 A&B Parallel 3.4 Series Parallel 6.7 Figure 12: Measured resistances between 3 different bulbs, along with comparison between series and parallel Calculations & Graphs Data collected for tables one and three were all done through a measured system; therefore, no calculations were needed. However, table two requires calculations to be done with the information provided. From equation two, three, four, and the data supplied in table 2 we can calculate the theoretical Req for all four circuit diagrams: Circuit Diagram 1: R eq=R1 + R2 Equation 2 ¿ 560 Ω+330 Ω ¿ 890 Ω Circuit Diagram 2: ¿ 1 1 1 = + Req R1 R2 Equation 3 1 1 + 560 330 ¿ 207.6 Ω R 1 ( R2 ) +R3 R1 + R 2 Circuit Diagram 3 :R eq= ¿ Equation 2 and 4 560 Ω( 330 Ω) +100 Ω 560 Ω+330 Ω ¿ 307.6 Ω R1 ( R 2 ) +R3 R 1 + R2 Circuit Diagram 4 : R eq= ¿ ( {[ {[ ] } } ( 100 Ω+330 Ω ) ( 560 Ω ) +330 Ω (560 Ω) (100 Ω+330 Ω ) +( 560 Ω ) ] (100 Ω+330 Ω ) (560 Ω ) +330 Ω + ( 560 Ω ) ( 100 Ω+ 330 Ω )+( 560 Ω ) Equation 2 and 4 ) +100 Ω ¿ 383.3 Ω From equation one, the data supplied in table 2, and the voltage given as 15.00 V we can calculate the measured Req for all four circuit diagrams: Circuit Diagram 1: R eq= ¿ V I 15.00V 16.78mA ¿ 89 3.9 Ω Equation 1 Circuit Diagram 2: R eq= ¿ V I Equation 1 15.00V 68.8 mA ¿ 218.0 Ω Circuit Diagram 3 :R eq= ¿ V I Equation 1 15.00 V 47.4 mA ¿ 316.5 Ω Circuit Diagram 4 : R eq= ¿ V I Equation 1 15.00V 38.43mA ¿ 390.3 Ω From here we can calculate the percent difference with the use of the data between theoretical Req and measured Req: ¿ Circuit Diagram 1−4 : ¿ Theoretical Req −Measured R eq∨ [ (Theoretical Req + Measured Req ) 2 ∗100=% ¿ ] Diff erence Discussion In the series and parallel circuits section there was a slight difference between the theoretical values and the experimental values, and this was in part because of the resistance of connecting curves and internal resistance of battery. The sources of error in this experiment consisted of system error in the measurement of the 2nd and 3rd design, and this could be caused by miscalculation when solving for the resistance. The error could occur when setting up the circuit and not making the right type of system or an incomplete system which would not allow the proper flow of current. This could be minimized simply by checking the work done to find the resistance and checking the system before running the experiment. In the light bulb section of the experiment the brightness of two bulbs in series vary from the single lightbulb. This is because, in a series connection, the brightness of the individual bulbs diminishes as more bulbs are added to the chain, as the current must be shared amongst them. The current decreases as the overall resistance increases P = I^2R, so brightness will be low compared to a single bulb. In contrast, the brightness of two bulbs in parallel are like a single bulb. This is because, in a parallel connection, the brightness of individual bulbs remains constant as more bulbs are added to the ladder. Current increases and decreases R, the brightness will be constant compared to a single bulb. In the series parallel setup, the voltage stays the same, and more bulbs cause a decrease in resistance and an increase in amperes which leads to an increase in brightness. Conclusion The experiment verified that resistance can be determined in a multitude of ways and with that there are plenty of ways to make efficient circuits by combining series and parallel circuits. Determining that resistance can be found in more than one way can be proven by how Ohm’s Law can be derived into the power formula. Additionally, adding resistances in both series and parallel can determine the resistance of the circuit, and if that information is not provided then resistance can be found with the help of Ohm’s Law if voltage and current are known. In terms of precision and accuracy this experiment was very accurate and precise as the percent difference was well below 5% as the percent error were 4.887%, 2.852%, 1.817%, and 0.437%. The errors can be reduced even further if more accurate readings are given in terms of amperes or if a better machine was used to read at the 0.000001 ampere. Making circuits also proved that different forms of series and parallel can create a variety of circuit border. Depending on the task one can create a circuit board that suits their need, by either using series and parallel individual or by combing them to create a complex circuit.