Please complete all the graphs and questions in this assignment. Use the pictures below to help.

Table 1: Experimental Data: Resistors in Series Battery V1 Voltage 11 V2 Voltage 12 V3 Voltage I; V123 Voltage 1123 Voltage across R1 Current across R2 Current across R3 Current across entire Current (V) (V) through (V) through (V) through circuit (V) through What do you notice if you compare all of the currents for a given voltage setting? Is this what you expected? What is the relationship between the voltages? Fill in Table 2 below, using the data from Table 1, and the following relationships: V V V V R1 = _13R2 = _2 iRS = 'IsiRs.exp = 123 3 123 FRs,theoretica = R1 + R2 + R3 1'1 1'2 From our initial setting, we expect R; = 25 + 50 + 100 = 13"50. If the equations are correct, then the theoretical and experimental values for Rs should be the same. Calculate the percent different between them: did the experiment work? How close is the theoretical resistance to 1759? Table 2: Analysis: Resistors in Series Battery Voltage (V) 10.0 20.0 % difference Do your experimental values for R1, R2 and R3 agree with the values you set them to be when you made the circuit? Are they dependent on the battery voltage? Why or why not? Drag the voltmeter so that you have one probe on either side of an ammeter. What is the voltage drop across an ammeter? What does this mean about its resistance? What do you notice about all of the currents? Is this what you expected? What is the relationship between the voltages? Is this what you expected? Fill in Table 5 below, using the data from Table 4, and the following relationships: V1 V_2 V_3 L123 1 1 1 _)_1 R1 = 11:R2=T2:=R3 T3 iRp,exp_ = {123 :R ntheor'etimi = (Rl + 5+ R3 1 From equation 6, we expect aneoretim; = (i + 510 + Tie) = (0.07)'1 = 14.39. If the equations are correct, then the theoretical and experimental values for RF should be the same. Calculate the percent different between them: did the experiment work? How close is the theoretical value for Rp to 14.30 Table 5: Analysis: Resistors in Parallel Battery R] (0) R2 (Q) R; (Q) Rp.exp(n) Rp.theury 0/0 Voltage (0) difference Do your experimental values for R1,R2 and R3 agree with the values you set them to be when you made the circuit? Are they dependent on the battery voltage? Why or why not? Finally, with your circuit still set up, you will record only the voltage and current across the entire circuit. To do this, drag the red probe of the voltmeter to the bottom left corner and the black probe to the bottom right corner. The \"total current\" will be read from the ammeter attached to the battery. Now click on each resistor to set their values to the values shown in Table 6 below. Record the total V 1 1 1 '1 voltage and total current. Then calculate Rp.xex 9:1122: Rplmeormm; = (R + a + F) for these 1231 2 3 resistance combinations. Table 6: Total Resistance for different combinations Resistance V123 (V) 1123(A) Ramada) Rp.1heury() Rl=100,R2=50,Ra=75 R [=50,R2=50,R3=50 Rl=25,R2=50,R3=?5 where 35 is the equivalent resistance of the resistors in series. That is, the three resistors in series could be replaced by a single resistor with a value of Rs, and the same current [would flow from the source: R5=R1+R2+R3 (3) B. Resistances in Parallel Resistors are said to be connected in parallel when connected as in Fig. 2. (In this arrangement, all the \"heads" are connected together, as are all of the \"tails\"). a - + Junction 1 o Junction 2 Figure 2. Parallel circuit The voltage drops across all the resistors are the same and equal to the voltage V of the source. However, the current I from the source divides among the resistors such that l=11+12+l3 (4) The current in an electrical parallel circuit divides according to the magnitudes of the resistances in the parallel branches, i.e. the smaller the resistance of a given branch, the greater the current through that branch. The current through each resistor is given by Ohm's law ( I = VfR,), and Eq.4 may be written as =++ (5) where RF is the equivalent resistance of the resistors in parallel. That is, the three resistors in parallel could be replaced by a single resistor with a value of RP, and the same current I would ow from the source: 1 1 1 1 F'F+F+? '9 Resistors in Series and Parallel Introduction In a previous experiment you have experimentally veried Ohm's law (V=IR). Now we will use Ohm's law to study electrical circuits. The components of simple circuits are connected in series andr'or parallel. Each component may be represented as a resistance to the ow of current in the circuit. In computing the voltage and current in the circuit (or part of the circuit), it is necessary to know the equivalent resistances of the series and parallel arrangements. In this experiment, the circuit characteristics of resistors in series and parallel will be investigated. After performing this experiment and analyzing the data, you should be able to: 1. Describe the currentvoltage relationships for resistances in series. 2. Describe the currentvoltage relationships for resistances in parallel. Background, Theory and Applications A. Resistances in Series Figure 1. Series circuit Resistors are said to be connected in series when they are connected as in Fig.1. (The resistors are connected in line or "head to tail"). When they are connected to a voltage source V and the switch is closed, the source supplies a current I to the circuit. By the conservation of charge, this current I ows through each resistor. The voltage drop across each resistor is not equal to V, but the sum of the voltage drops is. V=V1+V2+V3 (1) The voltage drop across each resistor is given by Ohm's law (V = IR) and Eq. 1 may be written as V=V|+V2+V3=IR1+IR2+IR3=I(R|+R2+R3)=IR5 (2) 3. Click on each resistors to change their values by sliding the bar at the bottom of the screen: set the one on the le (Resistor l) to 25.0 ohms, the one at the top (Resistor 2) to 50.0 ohms and the one at the right (Resistor 3) to 100 ohms. Notice that their values show up on the screen, and the color of the lines on the resistors changes as well, to reflect the color coding of resistors. 4. Click on the battery to set its value to 10.0 Volts. Note that it is set to have an internal resistance of 0.00 Ohms. 5. Be careil to check that none of your junctions have a red circle, that means that the connection is not made, and current will not flow. 6. At the bottom right, toggle between lifelike and schematic to see how the picture changes. Leave it in the setup which with you feel most comfortable. You are now ready to perform the experiment. To start the current owing, close the switch by dragging the handle so that it is in line with the circuit. You will then see the little blue dots (which represent negative charges) owing through the wires. Now measure the voltage across and the current through each of resistors 1, 2 and 3 and record them in Table 1. The current will be read from the ammeter connected directly to each resistor. To read the voltage, pull the voltmeter from its box on the right onto the screen, and drag the red probe on the voltmeter to one side of the resistor and the black probe to the other side. Make sure you get a positive reading: you may have to reverse the order of your red and black probes to do this. You will also need to record the voltage and current across the entire resistor circuit. To do this, drag the red probe of the voltmeter to the bottom left comer and the black probe to the bottom right corner. The \"total current\" will be read from the ammeter attached to the battery. Change the battery voltage to 20, 30, and 40 volts and repeat. Finally, with your circuit still set up, set your battery voltage to 100V by clicking on it. You will record only the voltage and current across the entire resistor circuit. To do this, drag the red probe of the voltmeter to the bottom left corner and the black probe to the bottom right corner. The \"total current\" will be read rorn the ammeter attached to the battery. Now click On each resistor to set their values to the values shown in Table 3 below. Record the total iRs.thecretica = R1 + R2 + R3 for these V12 a voltage and total current. Then calculate Rs.exp = I 123 resistance combinations. Table 3: Total Resistance for different combinations Resistance (0) R1=10032=5033=75 Ri=50,R2=50,R3=50 Ri=25,Rz=50,R3=75 Part 2: Resistors in Parallel 1. Now rearrange the same components from the rst part to connect the three resistors in parallel. To disconnect two items from each other, click on the circle betWeen them and hit the scissors icon to disconnect the junction. You may need to grab more wires to make this circuit. If it is easier for you, hit the RESET ALL button and start from scratch. 2. Make sure that your three resistors are arranged EXACTLY as shown in the gure below (look at the color bars), or your results in the table will be incorrect. R1 (25 ohms) should be in the lowest branch, R2 (50 ohms) should be in the middle branch and R3 (100 ohms) should be in the top branch. Change the battery voltage back to 10V. 3. Be careful to check that none of your junctions have a red circle: that means that the connection is not made, and current will not ow. 4. At the bottom right, toggle between lifelike E] and schematic to see how the picture changes. Leave it in the setup which with you feel most comfortable. Procedure: Part 1: Resistors in Series. We will use a PHET applet to create a circuit with three resistors connected in parallel and use it to determine the voltage and current through each of the resistors as well as the total effective resistance of the circuit. 1. Go to: h 53'] het.colorado.edufsims/htmla'circuitconstructionkitdcvirrual labflatestfcircuitconsuuction-kitdc-virtual-lab en.html A screen will load that looks like the following: Tick \"Values\" in the top box. 2. From the white menu at the left side and the meter box on the right, grab and assemble a battery, a switch, 3 resistors, 4 ammeters and as many wires as you need to create the circuit shown below. If you want to get rid of an item, click on it and then hit the trash can logo that appears at the bottom of the screen. To disconnect two items from each other, click on the circle between them and hit the scissors icon to disconnect the junction. If you want to get rid of it all and start again, click reset Show Current Electrons Wire 100.0 0 Conventional Current 0.00 A Labels Values Battery Voltmeter Ammeters 50.0 0 Current Light Bulb 10.00A + Wire Resistivity Resistor + Battery Resistance 25.0 0 Switch Current 1 0.00 A 10.0 V Current 0.00 A Tap circuit element to edit. You are now ready to complete the experiment. To start the current flowing, close the switch like you did in part 1. You will then see the little blue dots (which represent charges) flowing through the wires. Now record the voltage across and the current through each of resistors 1, 2 and 3 in Table 4. The current will be read from the ammeter connected directly to each resistor. To read the voltage, drag the red probe on the voltmeter to one side of the resistor and the black probe to the other side. Make sure you get a positive reading. You will also need to record the voltage and current across the whole circuit. To do this, drag the red probe of the voltmeter to the bottom left corner and the black probe to the bottom right corner of the circuit. The "total current" will be read from the ammeter attached to the battery. Change the battery voltage to 20, 30 and 40 volts and repeat. Table 4: Experimental Data: Resistors in Parallel Battery Vi Voltage I1 V2 Voltage 12 V3 Voltage 13 V123 Voltage I123 Voltage across R1 Current across R2 Current across R3 Current across entire Current (V) (V) through (V) through (V) through circuit (V) through RI (A) R2(A) R3(A) battery (A) 10.0 20.0 30.0 40.0 7