The Comparing Measured and Theoretical Values of V, I, R in Series and Parallel Arrangement - Lab Report Example

To compare measured and theoretical values of V, I, R in series and parallel arrangement Introduction The aim of this experiment is to compare the measured value of voltage, current and resistance arranged in parallel and in series using Kirchhoff’s and Ohm’s law(Wright, 2011). The aim of this experiment was achieved by arranging voltage, current and resistance in series and parallel, and the values of resistance, voltage and current measured in both series and parallel arrangemnts.For the accuracy the experiment is repeated three more times. Voltage This is the electric potential difference per unit charge in a complete circuit and it is measured in volts Current Current is the movement of electric charge in electric circuit, the charge which is carried by flowing electrons in a wire. Resistance This is the opposition of the flow of an electric current through a conductor in a complete circuit Series arrangement of the circuit For the series arrangement, current only has one path to follow thus it will be equal in any part of the circuit, that is IT= I1= I2= I3.Since it is a series arrangement, the electromotive force supplied by the power supply that is, the total voltage will be equal to the summation of the volts through the respective resistance (Wright, 2011) .Kirchhoff’s loop will yield VT = V1 + V2 + V3.This is illustrated as bellow. R1 I VT R3 R2 Parallel arrangement of circuit For the parallel arrangements there is more than one path for the current to follow, thus here the potential difference across the resistance will be equal, and the total current will be the summation of the individual currents across the resistance. Since V= IR, R =V/I (Wright, 2011). IT I1 V2 VT V1 R2 I2 R3 I3 That is VT = V1 = V2 = V3 IT= I1 + I2 + I3 Kirchhoff’s first law Kirchhoff’s first law generally shows that the total current ingoing a connection must be equal to the current leaving that connection (Paul, 2001. That is to say current in = current out and there is the conservation of charge. Taking into consideration a parallel circuit connection, current in = current out (IT= I1 + I2 + I3). Kirchhoff’s second law The second principle say that in any path about a circuit, the total of the emfs = the total of the potential differences. But since Pd = V = IR, so from the second law ∑pd = ∑IR. In other words we can say that the energy around the circuit is conserved (Paul, 2001). In other words can still states that the arithmetical summation of variations in the potential differences around a closed circuit path is zero. Ohm’s law Ohm’s law is concerned with the connection between current and voltage in an ideal conductor. It states that the voltage through an ideal conductor is directly proportional to the current through that conductor (Simon & Szwarc, 2001). That is, IR =V, where R = the constant of proportionality. Any material obeying that law is called Ohmic or linear material. From V=IR, we can get R=V/I V, I and R arranged in series Apparatus Resistors Connecting wires Ammeter Voltmeter Digital power supply Circuit box Procedure The provided resistances R1, R2 and R3 were measured and values recorded. The circuit set up was arranged as shown above, the voltage across R1, R2 and R3 were measured one at a time by replacing the voltmeter terminals across the resistor. The ammeter was placed in series in the circuit, the circuit opened at one of the connections to put the ammeter at the open ends. The current was read through the circuit and voltage through the resistor and values recorded. The experiment was repeated for two more trials, and the circuit disconnected after the experiment (Tobin, 2007). V, I and R arranged in parallel Apparatus Resistors Connecting wires Ammeter Voltmeter Digital power supply Circuit box Procedure The values of R1, R2 and R3 were measured and recorded in the table The circuit was arranged as shown, the voltmeter placed across the junction points and voltage across the resistance was measured. Taking into consideration that the voltage is the same in parallel arrangement. The ammeter was placed in along each resistor and the current in that branch recorded. The connections are opened at one end and ammeter placed between the open ends, the ammeter value are measured in (mA). The main current reading was taken that is, the current between the batteries, it is the current that leaves the battery at one terminal and goes in through the other terminal. The experiment was repeated for some two trials and values recorded. The circuit was then disconnected to protect the batteries. Results: Nominal Resistance (Ω) Measured Resistance (Ω) % Difference R1 = 680 671 1.3% R2 = 1000 978 2.2% R3 = 820 810 1.2% Rtot = 2500 2466 1.4% Series arrangement table Quantity Measured value from DMM Theoretical predictions % Difference Vs 15V 15V 0 Rtot 2466Ω 2500Ω 1.4 VR1 4.1V 4.12V 0.5 VR2 5V 4.97V 0.6 VR3 5.99V 6.07V 1.15 IA 6.075A 6A 1.25 IB 6.075A 6A 1.25 IC 6.075A 6A 1.25 ID 6.075A 6A 1.25 Parallel arrangement table Quantity Measured value from DMM Calculated Values Vs 10.1V 10V VR4 10.1V 10V VR5 10.1V 10V VR6 10.1V 10V IA 37.2mA 36.9mA IB 10.24mA 10.5mA IC 12.38mA 12.19mA ID 14.99mA 14.7mA Rtot Discussion Series arrangement From the series arrangement the measure value of current I is the same across the resistance R1, R2 and R3, which agrees with the theoretical explanation of the circuit series arrangement. But when comparing the measured value of V, I and R with the theoretical values there are slight differences (Tobin, 2007). For instance the measured value of I1, I2 and I3 are all 6.075A but the predicted theoretical values are all 6.00A, which carries on to the measured and theoretical values of V and R, the nominal resistance of R1, R2, R3 are 680, 1000 and 820 while the measured values are 671,978 and 810 respectively, and V1, V2 and V3 showing the same differences in the measured and theoretical values ,where the measured values are 4.1v, 5v and 5.99v and theoretical values are 4.12, 4.97 and 6.07 respectively. Conclusion The differences between the theoretical values and the measured values resulted from the experimental errors which included parallax or random error which results when there is some distance between the measuring scale and the indicator used for measurements, it may have also resulted from environmental factors, physical variations or instrument resolution, that is the exactness that confines the capability to resolve the small measurement alterations. Parallel arrangement From the theory, in parallel circuit arrangements the value of V is always the same across all the resistance and the value of current varies with the total current being the summation of the individual currents. Concerning the carried practical the measured value of voltage is 10.1V which is the same across all the resistance (Tobin, 2007).But comparing the measured values of voltages and currents to the theoretically predicted values there is some slight differences. Thus the measured values of currents and voltages are different. That is I1, I2 and I3 measured are 37.2, 10.24 and 12.38 while the theoretical values are 36.9, 10.5 and 12.19 respectively. There is also some differences between the total measured resistance and the total theoretical resistance which is 1.4 percent that is, │ (2500-2466)/2500│x 100. Conclusion These differences may have resulted from the experimental errors which included parallax or random errors that resulted when there was some distances between the measuring scale and the indicator used for measurements, it may have also resulted from environmental factors, physical variations or instrument resolution that is the exactness that confines the capability to resolve the small measurement alterations. Improvements on the method By repeating the experiment several times we shall have reduced the chances of inaccuracy. Minimizing the distance between the measuring scale and the indicator used for measuring that is, to position yourself in a better position which facilitates correct measurement takings. Taking the experiment in an environmentally friendly place or laboratory to minimize the harsh conditions, this may be done by closing the windows, and lastly by making sure that the voltmeters and ammeters used are not faulty. References: Henry, T. (1996). Ohms law, electrical math and voltage drop calculations. Orlando, FL: Henry Publications. Zandman, F., Simon, P., & Szwarc, J. (2001). Resistor theory and technology. Malvern, PA: Vishay Intertechnology, Inc. ;. Paul, C. R. (2001). Fundamentals of electric circuit analysis. New York: John Wiley & Sons. Tobin, P. (2007). PSpice for circuit theory and electronic devices. San Rafael, Calif.: Morgan & Claypool Publishers. Wright, V. E. (2011). Circuit analysis. New York: Nova Science Publishers. Gibilisco, S. (2006). Teach yourself electricity and electronics (4th ed.). New York: McGraw-Hill. Read More