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Lab Report

Resistors in Series and Parallel Objectives Investigate the series and parallel combinations of resistors. Apparatus Two resistors Ri and R2, multimeter, DC power supply Introduction Part 1: Resistors in series In the first part of this experiment we will study the properties of resistors, which are connected "in series". Figure shows two resistors connected in series. When two or more resistors are connected together such that they have only one common point per pair of resistors, they are said to be in series, as shown in figure below. The current / is the same through each resistance. Since the potential drop from a to b equals /Ri, and the potential drop from b to c equals /R2, then the potential drop from a to c is: V = IR1 + IR2 = I(R1 + R2) = IRequivalent We can replace the two resistors by a single equivalent resistance Requivalent, whose value is the sum of the individual resistances: Requivalent = Ri + R2 In general, if n resistances are connected in series, then their equivalent resistance is: Requivalent = Ri + R2 + R3 + + Rn Part 2: Resistors in parallel Two or more resistors are said to be connected in parallel if they are connected as shown in Figure below. They have two common points per pair of resistors. In this case there is an equal potential difference across each resistor, but the current in each resistor branch is generally not the same. The current / splits into /1 and /2 at the junction (point a) such that: I = 1 + 12I = (V/Ri) + (V/R2) = V/Requivalent From this result, we see that the equivalent resistance is given as: 1/Requivalent = (1/Ri) + (1/R2) In general, the equivalent resistance for n resistances connected in parallel is: 1/Requivalent = (1/Ri) + (1/R2) + (1/R3) + ... + (1/Rn) Procedure 1) Connect the two resistors Ri and R2 in series and note that the ammeter is connected in series with both resistors and power supply, while the voltmeter is connected in parallel to both resistors (as shown in Figure 1. 2) Vary the voltage in the power supply and obtain at least five pairs of readings of the current (I) and the potential difference (V) across the resistor Req (Check the lab video and record the values in a table) 3) Connect the two resistors Ri and R2 in parallel and repeat step (2) with / representing the current in the circuit and V representing the potential drop across the common points of Ri and R2. (Record these in a table) 4) Plot two curves of current (/), as the independent variable, and voltage (V), as the dependent variable, on the same graph. 5) From the graphs determine Req for series Rs and parallel Re cases. 6) Compare your results of Req in both cases with their corresponding values found using equations above. (Measured values of these resisters found in the video) Questions 1) What conclusion can you draw, about the values of the total resistance in the case of series connection (Rs) and parallel connection (RP)? 2) A set of lamps are connected in series. What happens if one of them burns out? Explain your answer (Use a diagram). 3) Another set of lamps are connected in parallel. What happens if one of them burns out? Explain your answer (Use a diagram).Connection on Breadboard The breadboard has many tiny sockets or holes arranged on a 0.1" grid. The leads or terminals of most of the components like resistors, diodes, transistors, etc. can be pushed straight into the holes to make a connection. Letters are used on the breadboard to identify horizontal rows and numbers are used to identify vertical columns. The lines which are connecting the holes show how some vertical columns and horizontal rows are internally connected. When a voltage is applied to the breadboard current can flow along these internal connections. Each column of five sockets in the inner sections is electrically connected to the others. The two outer sections of the breadboard are usually used exclusively for power. DOO0 0 000 00 0000 0 DO000 000 0 0 0 0 0 0 0 + DO000 00 0 0 0 DO00 0 000 0 0 + 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 00 DO0 00 DO000 0 0 0 00 00000 00 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 DO0 0 0 DO0 00 FGHI F G CDE 0 0 0 0 10 0 0-0 ABCDE D0 0 0-0 DOO0 0 DOOOO .0 000-0 NOOOOO 40 0000 6000 00 80 0 0 0 0 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 DO0 0 0 00 00 0 00 0 0 0 00000 00000 0000 0 + OOOOO OOO00 00000 000 0 0 + +Appendix A - Resistor Color Coding Black 100 Brown 101 Red 102 Orange Yellow DOYOUAWNGO ONanAWNEO Green Blue Violet Gray 108 White 10 Color codes for the accuracy of a standard resistor. If the extra band is SILVER the accuracy is 10%, for GOLD the accuracy is 5%. Example: How to find the value of a resistance from the color codes. There are four color strips; one of them is far from the other three. This one must be used to estimate the uncertainty in the resistance. In figure A.1, the first strip is yellow which corresponds to number 4 in the table above. The second one is blue which corresponds to number 6. The third is green which corresponds to mumber 5. The fourth strip is silver which corresponds to 10%. The accuracy in this resistance is: AR = 14.6x10* x10% =14.6x10'n =1460102 . So, R # AR= 4.6x10 14.6x10'n Yellow Blue Green Silver Figure A.1. The value of this resistance is: R= 4.6x10*0