The Resistors and Logic Circuits - Lab Report Example

RESISTORS AND LOGIC CIRCUITS The primary experiment objective is to study the flow of current and voltage drops in different circuit connections and the operation of fundamental logic circuits. Resistors, representing loads in contemporary electrical circuits, were connected in series and then in parallel and the circuits were powered with a d.c supply. Voltages across the resistors and currents in the different circuit configurations were measured and compared with expected theoretical values. Diodes were used to simulate the logic circuits of AND and OR and the circuit operation on biasing the diodes iteratively was consistent with the theoretical expectation. The results for the resistor circuits also closely approximated theoretical calculations. Introduction In an electric circuit, voltage is the difference in potential energy (in terms of electric charge) between two points in the circuit while current is the rate of flow of charge past a point in the circuit. According to Theraja (2004), resistance is the property of substance through which it opposes (or restricts) the flow of electricity (or electrons) through it. Electric resistance is analogous to friction in mechanics. An electric circuit is usually a full path for current to flow from the positive power source terminal to the negative terminal. The circuit can be series or parallel. If there is just a single path for current to flow then the circuit elements are connected in series, whereas if there are a number of alternative current paths with identical voltage existing across the paths then the circuit is in parallel connection. For calculating the equivalent resistance of a complex network of resistors, as well as the current flowing in the various conductors, Kirchhoff’s laws are used. They are two in number; Kirchhoff Current Law (1st Law) states that in, the algebraic sum of the currents meeting at a point (or junction) in an electric network adds up to zero. Considering the network above, we have; Incoming currents=outgoing currents I1 + (-I2) + (-I3) + I4 + (-I5) =0 I1+I4=I2+I3+I5 Thus at a junction; =0 This helps to calculate currents in the various conductors. Kirchhoffs Voltage Law (2nd Law) states that the algebraic sum of the products of the currents and resistances in every conductor of a closed path (or mesh) in a network and the algebraic sum of respective e.m.fs in that path adds up to zero. That is + = 0 around a mesh. Studies have proved that provided that provided the resistance in a circuit is constant, and the flowing current has a direct proportionality to the difference in potential across the ends of the conductor. This has a definition by Ohms Law which argues that the ratio of the potential difference (V) between the conductors two points to the respective current (I) flow between is a constant; given the temperature of that there is no change in a conductor. = constant or =R Logic circuits are electronic circuits that make logical decisions. They are built using gates that consist of one output and one or more inputs. The output signal depends on the specific combination of inputs. The building blocks of most digital systems such as computers and calculators are the logic gates. They apply the logical algebra developed by George Boole (Boolean algebra) to implement the logic function of the hardware. The AND and OR gate are some of the fundamental logic gates. The OR gate; A + B=C The figure above depicts the symbol of the OR gate. The OR gate has an output of 1 when either A or B or both are 1. It is an any-or-all gate because there is an output when any or all the inputs are present. There is a zero output if and only if all the inputs are zero. A B X 0 0 0 0 1 1 1 0 1 1 1 1 Truth table for the OR gate The AND gate; A. B=C Symbol of the AND gate The AND gate has an output of 1 only when both inputs are present, and that is, when A and B give an output of 1. Therefore, it an all-or-nothing gate where all inputs has to be present for there to be an output. A B X 0 0 0 0 1 0 1 0 0 1 1 1 Truth table for the AND gate Method Experimental setup for the series circuit; . The three resistors were first measured using the digital multimeter (DMM) in ohmmeter mode, and their values tabulated. They were then connected in series on a breadboard. The total resistance Rtot was measured before powering the circuit and it was tabulated for percentage deviation calculation. The variable dc power supply was connected and the output was adjusted to 15V with the help of the DMM in voltmeter. This value was recorded. The voltage drop across each resistor, that is, across points A-B, B-C and C-D, was measured and tabulated. Current test; The DMM was then set up in ammeter mode and currents at various points in the circuit were measured. This involved breaking the circuit and remaking it in order to insert the ammeter at points A, B, C and D. The results were tabulated. Experimental setup for the parallel circuit; The connection of the circuit is as shown in the above circuit diagram. The DMM was used to measure the individual resistances R1, R2, R3 and the total resistance Rtot. All the currents and voltages associated with the circuit were then measured with DMM connected in the respective configuration. The values were tabulated. Testing logic circuits; The OR gate; The circuit was connected as shown above. The inputs A, B and C were connected to O V supply representing logic 0 or 5 V representing logic 1, following the input combinations shown in the table below; A B C Y 0 0 0 0 0 1 0 1 0 0 1 1 1 0 0 1 0 1 1 1 0 1 1 1 The values of Y were measured for all possible combinations of the inputs A, B and C. A variable 0-20 V dc power supply set to 5 V was used for this test and the DMM was used for measuring. AND gate test; The circuit was connected as shown above. The inputs A, B, and C were connected to O V supply representing logic 0 or 5 V representing logic 1, following the input similar to those of the OR gate. The values of Y were measured for all possible combinations of the inputs A, B and C. A variable 0-20 V dc power supply set to 5 V was used for this test and the DMM was used for measuring. Results; Series circuit; Table 1; Table of nominal resistance Nominal Resistance () Measured Resistance () % Difference R1=680 672.5 1.13 R2=820 812.1 0.963 R3=1000 979.3 2.07 Rtot =2500 2463.9 1.44 Table 2; Table of measured values of V, I and R. Quantity The value measured from DMM Using DMM to predict theoretical values for sR and Vs % Difference Vs 15 15 0 Rtot 2463.9 2463.9 0 VR1 4.0974 4.035 1.546 VR2 4.9455 4.8726 1.496 VR3 5.963 5.8758 1.484 IA 6.089 6 1.483 IB 6.090 6 1.500 IC 6.095 6 1.583 ID 6.091 6 1.517 Parallel circuit; Table of measured values of V, I and R. Quantity Measured value from DMM Calculated values Vs 10.065 10 V VR4 10.064 10 V VR5 10.065 10 V VR6 10.065 10 V Ia 37.517 mA 36.901 mA Ib 10.285 mA 10 mA Ic 12.4101mA 12.195 mA Id 14.999 mA 14.705 mA Rtot 254.43 270.995344 Logic circuits; Results for OR gate; A B C Y 0 0 0 0 0 0 1 1 0 1 0 1 0 1 1 1 1 0 0 1 1 0 1 1 1 1 0 1 1 1 1 1 Results for AND gate; A B C Y 0 0 0 0 0 0 1 0 0 1 0 0 0 1 1 0 1 0 0 0 1 0 1 0 1 1 0 0 1 1 1 1 Discussion; The results proved that current in a series circuit remains constant from one point and back. The voltage drops across the successive resistances from the positive terminal of the power source to zero at the negative terminal this was an agreement with Kirchhoff’s voltage law. The minimal percentage difference between the measured values of voltage across resistances and the theoretical values show that there is a linear relationship between the voltage and current across the resistances and therefore Ohm’s Law was satisfied. There percentage difference existing between the nominal resistance values and the measured values. There was a slight difference between the measured potential difference across the resistors and the expected theoretical values. This was due to the difference in the nominal values of the resistors and the actual measured value. The measured values of voltages across resistors in the parallel circuit proved that the voltage across alternative paths in a parallel circuit remains constant with the current dividing across the paths according to the current divider rule. This agrees with the theoretical expectation. The calculated total equivalent resistance in parallel connection and the measured total equivalent resistance differed slightly. This, together with the difference of resistances from nominal values caused the difference that was obtained between measured values of current flowing in the resistors and the expected calculated values. The results from the logic circuits were also in agreement with the theoretical truth tables. Conclusion; The experiments confirmed that current in a series circuit remains constant while the voltage drops across the circuit to an algebraic sum of zero in accordance with Kirchhoffs Voltage Law. There was also a linear relationship between the voltage drop and current flowing through each conductor and therefore Ohms Law was applicable in finding the voltage drop across each resistor. On the other hand, in a parallel circuit, the voltage across each path is constant and the current divides between the paths. The current in each conductor terminating at a node can be found using the Kirchhoffs Current Law. The simulated logic gates showed that logic circuits perform some logical operation on the inputs and the output depends on the specific input combination. Appendix 1. Calculation for table 1; % Difference= x 100% 2. Calculation for table 2; Theoretical prediction of = Measured resistance x theoretical expected current Voltage drop across resistors % Difference= x 100% 3. Calculation of total equivalent resistance; Given three resistors, R1, R2, R3, total resistance Rtot = Expected calculated values of currents in each path = References Hyper Physics, viewed April 14, 2015, < http://hyperphysics.phy-astr.gsu.edu/hbase/electric/elecur.html> SparkFun Electronics, n.d., Voltage, Current Resistance and Ohm’s Law, viewed April 14, 2015, < https://learn.sparkfun.com/tutorials/voltage-current-resistance-and-ohms-law> Theraja, B L & Theraja, A K 2004, A Textbook of Electrical Technology, 24th edition, S. Chand & Company Ltd, New Delhi. Tokheim, R L 2002, Digital Electronics, Principles and Applications, 6th edn, McGraw-Hill, Glencoe. Read More