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1 Phys 3 Lab 7 Ch 0 Simple DC and RC Circuits Equipment: power supply, banana cables, circuit board, switch, 0, 70, 460, & 30, k,two multi-meters, differential voltage probe, Phys 3 experiment kits: batteries and holders, alligator-clip wires, bulbs and holders, and F capacitor. Objectives In this lab you will qualitatively and quantitatively demonstrate: Ohm s Law relating voltage, resistance, and current The Junction rule relating all current flowing into and out of a junction in a circuit The Loop rule relating the voltage drop around a closed loop in a circuit The capacitor s behavior sinking and sourcing charge facilitating current flow Overview Chapters 9 and 0 present microscopic and macroscopic perspectives on circuitry. Following their example, this lab asks you to construct basic circuits using batteries and light bulbs so you can see the effects of varying voltage, current and resistance. However, you ll also use a power supply, resistors, and digital multi-meters to get more quantitative. Instrumentation A digital multi-meter is the go-to tool for evaluating circuitry. It can measure resistances, currents, and voltages (both steady DC, and oscillating AC). In this lab, you will use two multi-meters like those pictured below (using two rather than just one is merely a convenience; either could do the other s job.) You will use the black one to measure current and the other (yellow) one to measure resistance and electric potential differences (voltage). Be careful to watch the units because they may adjust automatically as the readings change. V OFF V ~ 0 0m m 3.4 mv 500 0k k 0k ma AC V DC V ma/k COM BATT 9V.5V 0 ma k DCmA DCV. Ohmmeter: To measure resistance, turn the yellow multimeter s dial to 0 in the range (lower left). Only use the meter in this mode to find the resistance of an individual resistor, not on a circuit with current running through it. The probes from the multi-meter should be touched to either side of the resistor while the resistor is not in parallel with any other circuit element(s).. Voltmeter: Turn the yellow multi-meter s dial to 0 in the V range (upper left). The probes from the multi-meter should be touched to the two points between which you want to know the potential difference. A positive voltage reading means that the red probe is at a higher voltage than the black probe is; a negative reading means the reverse. 3. Ammeter: Turn the dial to DCmA and plug a wire into the ma/k socket. The ammeter must be inserted into a circuit so the current flows through it. A positive current reading means that the current is flowing into the wire connected to the DCmA socket and a negative reading means it is flowing in the opposite direction.

2 Ohm s Law I. Theory As Chapter 0 discusses, for Ohmic resistors, V= -IR, captures the interplay between the voltage drop (V) across a resistor, the resistance (R) across it, and the current flowing through it. The negative sign (neglected or avoided in most texts) reminds us that the direction of current flow is the direction of the voltage drop, just as the direction of water flow is downhill. Resistors are specific electrical devices that have been optimized to obey this relation. For something like a light bulb, this isn t strictly accurate (or, rather, the resistance is itself a function of the current), but it remains qualitatively true that increasing the voltage will increase the current. You can deduce the qualitative strength of current through a bulb from its brightness since a bulb s brightness reflects the rate with which it radiates energy which must be the rate with which energy is brought into the bulb by the electrons that speed through it. As you learned in Chapter 0, the rate with which energy is transferred to the electrons speeding through a potential difference, i.e. the power, is P = IV. Combining that with Ohm s law one way or another tells us that P = I R=V /R. So, for constant current, the brighter the bulb, the more resistive it is, or for constant voltage, the brighter the bulb, the less resistive it is. II. Qualitative Experiment In the Phys 3 experiment box, you ll find two D batteries and their holders, colored wires with alligator clips on the ends (they look like the name suggests), and little light bulb holders and two kinds of bulbs round and oblong. With one and then the other light bulb, wire-up the simple circuit that s illustrated. Note that in the two scenarios (with round or oblong bulb) you are providing the same voltage difference. So comparing their brightness, which bulb has the greatest resistance? According to Ohm s law, if you decrease the voltage applied across the bulb, you d expect less current to be driven through it and thus the bulb to be dimmer. To see this, move one of the wires so only one battery is across the bulb. III. Quantitative Experiment You ll compare the voltage drops across four resistors to the values you d expect according to Ohm s law. There are four resistors held in place by four springs (each of which is wired to a banana plug at the end of the board). The resistors are distinguishable by their color stripes: A) red-red-purple, B) red-purple-brown, C) yellow-purple-brown, and D) orange-orange-purple.

3 Phys 3 Lab 7 3. Set the yellow multi-meter for use as an ohmmeter and measure the resistance of each of the four resistors on the board. Enter your measurements in the first column of the table below. Measured Resistance () Measured Current (ma) Measured Voltage (V) Expected Voltage (from Ohm s law) (V) A) rd-rd-pr B) rd-pr-br C) yl-pr-br D) or-or-pr. To measure the current through and voltage across the first resistor, plug the unconnected red and black wires (from the power supply and the black multi-meter) into the first two banana plugs, turn on the black multi-meter (switch on the side) and the power supply ma Schematic DC V AC V k DCmA ma/k COM DCV Am p s 5 V - R 3.4 mv V OFF V ~ Vo lts BATT 0 0m m 0k k 0k 0 9V.5V 0 ma 3. Record the current through the resistor and voltage across it in the first row of the table. Just record the magnitudes, don t worry about the signs. Use Ohm s law to calculate the expected voltage from the measured resistance and current. 4. For each of the other resistors, turn off the power supply, and move each wire over just one plug on the board to connect to the next resistor, and then turn the supply back on. Again, measure the current and voltage, and calculate the expected voltages using the measured currents and resistances. Without getting into the uncertainties of multi-meter s measurements (often some percent of the measured value plus a percent of the scale the meter s set to plus in the last digit shown), it suffices to say that the voltages you directly measure and those you calculate using Ohm s law should be within five to ten percent of each other.

4 Phys 3 Lab 7 4 Loop Rule: Voltages and Resistors in Series I. Theory Kirchhoff s Loop Rule: The sum of the voltage steps around any closed loop in a circuit must equal zero. This follows logically from the fact that the electric potential energy for a charged particle at a given location is the same regardless of the path the particle took to get there. So if it travels around any closed loop back to its starting point, its net change in electric potential energy must be zero; divide by the object s charge, and you have that the corresponding change in electric potential must also be zero. Resistors in Series: Two resistors are in series if they have the same current through them. One consequence of the loop rule is that the voltage drop across a whole series of resistors is simply the sum of the voltage drops across each individual one. Putting these two ideas together with Ohm s law, V V V V V ser ser ser IR I IR R R So, for the given voltage, you d get the same current flowing if you had just one resistor with resistance R ser R R II. Qualitative Experiment Two light bulbs in series, as illustrated, would present the batteries with a resistance equal to the sum of their resistances. Should more or less current flow through the two bulbs rather than when there was just one bulb? Consider how that would affect the bulbs brightness. Wire up the circuit and see. Are the bulbs brighter or dimmer than if one or the other were individually wired up to the batteries? III. Quantitative Experiment. With the power supply and resistors, set up the circuit shown below by plugging the wire from the supply into the 4 th port and the wire from the black multi-meter into the st. You will measure the voltages between the points shown to test Kirchhoff s Loop Rule. R A 3 5 V - R B R C 4

5 Phys 3 Lab 7 5. Measure the voltages between each pair of points (plugs, where the black plug is number ) with a voltmeter by touching the black lead of the yellow multi-meter to the first point listed and the red lead to the second point. Record your measurements below being sure to include the signs. 3. The potential differences should add up to zero for a round trip around the circuit: V V V V V =0. Put another way, the three negative voltages should add up to be opposite the one positive voltage. Check that is the case (within a few percent.) 4. Based on the individual resistances that you d previously measured, what is the sum of the three resistances used, and thus the single equivalent resistance for the circuit? 5. If that is truly the equivalent resistance, then according to Ohm s law, it should equal the power supply s voltage divided by the current that s flowing through the circuit. According to the black multi-meter, what is that current? 6. What then is the ratio of the supply s voltage to that current? It should be within a few percent of the equivalent resistance you determined above. Junction Rule: Currents and Resistors in Parallel I. Theory Kirchhoff s Junction Rule: The sum of all currents entering a junction must equal the sum of all currents leaving that junction. This is simply a consequence of conservation of charge in the same way that conservation of cars would dictate that (in steady state) the rate with which cars enter an intersection must equal the rate with which they leave the intersection. So, if you have a power supply providing I sup current which splits up through umpteen parallel paths, I sup I I Combining this with Ohm s law and the loop rule (which tells us that the full voltage drop of the supply is applied across each parallel path individually), yields Vsup Vsup Isup R R V sup R R So, just as much current would be drawn from the supply if, instead of having the umpteen parallel resistances there were just one path with resistance R par R R

6 Phys 3 Lab 7 6 II. Qualitative Experiment To a pretty good approximation, the batteries maintain a constant voltage regardless of the load (unless the load has extremely low resistance, and so draws a lot of current.) So whether you attach one light bulb or two in parallel shouldn t significantly change the voltage that the batteries maintain. Wire up the illustrated circuit. Connect and disconnect one of the bulbs and observe the brightness of the other it shouldn t (hardly) change if the battery s voltage across and thus current through the bulb is unchanged. (In actuality, you may notice that the other bulb very slightly dims; se the text s section 0.4 for a discussion of batteries and their effective internal resistance.) III. Quantitative Experiment. Set up the circuit that s illustrated schematically to the left below and is illustrated a little more realistically to the right below. You ve probably already noticed the four little jumper wires connecting six springs on the circuit board; these will help. Move resistor A and resistor B to complete the circuit. The sharp ice pick can be used to wedge apart rungs of a spring to make room for inserting a resistor s leg. Plug the two cables into the last and third-from-last red ports (furthest from the black one) to connect the power supply to the bottom two springs. junction Sup B 5 V - junction Sup B A R A R B A To test Kirchhoff s Junction Rule, you will measure the currents into and out of the junction indicated with a dot.. Dial the yellow multi-meter to the ma position so it can measure current, then insert its two probe tips where the Sup wire s ends are and remove the Sup wire. Turn on the power supply, and the yellow multi-meter will measure the current provided by the supply into the junction. 3. Replace the Sup wire, and, in turn, do the same with the A wire to measure the current passing out of the junction to resistor A, and then the B wire to measure the current passing to resistor B.

7 Phys 3 Lab 7 7 According to the junction rule, the total current flowing out (I A I B ) should equal the current flowing in (I sup ). Your measured values may not be perfectly equal, but they should be within a few percent of each other. Capacitors: Charging and Discharging I. Theory Consider the circuit illustrated below. It is similar to that discussed in section 0.6 of your text. The switch initially connects the capacitor across the power supply and leaves the resistor dangling so the capacitor gets charged up. Then the switch is flipped to connect the capacitor across the resistor and leave the supply dangling. V sup - - switch C R Assuming negligible electric field in the connecting wires and corresponding voltage drop along the wires, the loop rule (from conservation of energy) tells us: V capacitor V resistor 0. Since V capacitor Q C and IR, we can write this as c V resistor Q c C IR 0. Where I dqr dt is the rate with which charge flows through the resistor. Rather subtly, while the capacitor is discharging, every morsel of charge that flows through the resistor is a morsel that flows off the capacitor, thus reducing the capacitor s charge: dq dq. So the current through the wire can be rephrased as as I dq dqc dqc Qc C R 0 or RC Qc. dt dt c c dt. Thus, the relation can be written The latter form says the rate with which the charge on the capacitor decreases is proportional to the amount of charge on the capacitor. This is a differential equation describing the decrease in charge on the capacitor as a function of time. Later in your career you ll get familiar with solving such equations, but for now it suffices to say that this particular equation is solved by Q c Q e o t RC (plug this in for Q c in the equation and see that you get a true statement). R

8 Phys 3 Lab 7 8 Since the voltage drop across the capacitor is proportional to the charge on the plates, V Q C, we similarly have c c / t RC V0 e, V c where V 0 is the initial voltage difference across the capacitor at time t = 0. That would be the supply s voltage if t = 0 just when the switch is flipped. The combination RC is the exponential time constant for the circuit (Ohm*farad = second). Qualitatively, the larger it is, the longer it takes for the capacitor to discharge. II. Qualitative Experiment As a capacitor discharges across a light bulb, the voltage across capacitor and bulb exponentially decays, and so must the current and radiated power, thus brightness diminishes. How long that takes depends on the capacitor-resistor s RC time constant, and thus scales with the bulb s resistance.. Wire up one of the circuits illustrated using the round light bulb and paying special attention to the capacitor s orientation the long leg must be connected to the terminal.. Switch between the two circuits illustrated. When you do so, the bulb will immediately brighten and then gradually dim. Roughly time that dimming (you don t need to be terribly precise counting in your head will suffice.) This will give you a ballpark for the RC time constant of the bulb capacitor combination. 3. Now repeat but using the oblong bulb. With which bulb does the capacitor take longer to discharge? Check that that s consistent with your very fist answer in this lab (to the question of which bulb is more resistive).

9 Phys 3 Lab 7 9 III. Quantitative Experiment You re going to charge a -farad capacitor with the batteries and then discharge it across a k resistor. You ll use LoggerPro to monitor the voltage for 0 minutes.. In the light bulb capacitor circuit you just explored, set it up once more to charge the capacitor (as illustrated on the left).. After the capacitor is charged (the bulb s dimed out), replace the bulb with the k resistor (brown black red). 3. Plug a differential Voltage Probe into LabPro; Clip the black lead of the probe to the negative leg of the capacitor (on the side of the capacitor marked with a white stripe and with the short leg) and the red lead to the other leg of the capacitor. 4. Open the Capacitor file from the Physics Experiments/Phys 3 folder. 5. Switch the circuit to the other configuration so the capacitor begins discharging, and immediately hit the green collect button. 6. Once the data has been collected, you can tell Logger Pro to do an exponential curve fit. To do that, select Curve fit from the Analyze menu, and define an exponential function of the form A*exp(-t/B); ask instructor for help. What s the exponential decay time? (note: since the time axis in minutes, you ll need to multiply B by 60 to get it in seconds.) 7. Disassemble the circuit and use the multimeter to measure the resistance of the -k resistor. Since the decay time should equal RC, and you have values for that time and for R, what must be the value of C? That should be within about 0% of the farad printed on it.

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