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Introduction to DC Circuits & Multimeters PS253 — Physics Lab for Engineers Embry Riddle Department of Physical Sciences Daytona Beach, Florida In this lab students learn how to use the current, voltage and resistance functions of a digital multimeter (DMM) and how to correctly connect the DMM to a circuit or component to measure these quantities. It is presumed that the student has mastered the use of Ohm’s law and series and parallel resistance formulas. The voltage and current in a circuit composed of a combination of series and parallel resistors will be measured and compared to the expected results. A controlled experiment will be conducted with a simple resistor and a light bulb in which current is measured as voltage is continuously increased. The results will be displayed graphically and compared to predictions from Ohm’s Law. Your graded work will consist of an in-lab worksheet and a post-lab worksheet. When asked to record anything you should be writing it on the in-lab worksheet (wkst). Digital Multimeter Operating Instructions Measuring Voltage: parallel meter connection ‘Voltmeter’ Voltage is defined as the electrical potential difference between two points. Because of this, in order to measure voltage you need two points of contact that will be at different electrical potentials. This is satisfied by connecting the DMM in parallel with whatever it is you want to find the voltage across. If you were to put the DMM in series, the meter’s contacts would essentially be next to each other with nothing in between them- hence at the same potential. Quick Tip: for voltage, don’t disconnect anything, just add the meter onto the circuit! To measure the voltage gain(drop) across a circuit component, plug a wire lead into each of the DMM sockets marked “COM” and “V” and turn the meter dial to the highest DC Introduction to Electricity & Circuits Physics Lab for Engineers voltage scale. With electrical power supplied to the circuit to be tested, simply touch each lead to a terminal on either side of the circuit component. Turn to successively lower voltage scales on the DMM until the best resolution is shown with a value on the display. Be aware that if your setting is too low and the voltage too high it will saturate and not give a reading. Some DMMs register this by only displaying a “1” or “-1” on the display, others might show “0”, and some may even make an audible alarm (especially on current settings). For example, if you are on a 2V setting it will only register voltages up to but not including two volts. If the voltage ends up being 5V you will need to turn to a higher voltage dial. This saturation level happens for all measurements on the DMM dials. Measuring Current: series meter connection ‘Ammeter’ Electrical Current is the flow of charged particles due to the presence of a potential difference between two connected points in space. In the case of a circuit, electrons will flow if there is a continuous connection of conductors between points of high and low potential (normally across two battery terminals or power supply terminals). Additionally, current will always want to flow along the path of least resistance, just like any other particle flow. Since current is a flow through one point, the DMM should always be in series at the point you want to measure current. If you tried to measure current with a DMM in parallel you introduce a split in the path and the current flow will be altered. More often than not all the current will suddenly flow through the DMM since there is very little resistance in the meter; this will break the meter and cause what is called a short circuit. Quick Tip: for current, you must disconnect a wire, then reroute through the meter! Plug wire leads into the DMM “COM” and “10A or 20A” sockets. Turn the meter dial to the 10A or 20A scale position. Disconnect one of the wires going to the component you wish to measure the current passing through. Connect one DMM wire lead to the component and the other to the circuit wire that was removed. If the DMM shows less than 0.2 amps change from the “10A or 20A” outlet to the “mA” socket and try successively lower current scales to obtain the best resolution. – Page 2 of 6 – Introduction to Electricity & Circuits Physics Lab for Engineers Be careful with using the milliamp “mA” socket as the DMM internal circuit to this scale setting has a limit to the current it can handle (normally 200-250mA). It is protected by a quick blow fuse if the current goes too high. Although this does protect the DMM from most damage, it does render the “mA” socket useless until a new fuse is put into the DMM. This wastes time and money! Measuring Resistance: meter across component, power source disconnected ‘Ohmmeter’ Electrical resistance is an opposition to the flow of current through a material. Resistance depends on the properties of the material: primarily composition, temperature, and shape. Resistance can be measured for one item, such as a single resistor, or a combination of items or an entire circuit. The DMM measures resistance by pushing a small test current through whatever it is connected to and comparing it to the output voltage it receives back. In order for this to work properly the test current has to be the only current, if a power supply or battery is connected it will overwhelm the test current and your readings will be wrong. Also keep in mind that the DMM measures the resistance of any and all components connected to it at the same time as long as current flows over all attached components. For example, if you place the ohmmeter across one resistor which is still connected in parallel with a second resistor you will be recording the effective resistance of both resistors. Plug wire leads into the “COM” and “V” sockets. Turn off all power supplies and disconnect all batteries. Disconnect one lead from the component you wish to test. Select the highest Ohm scale and switch to lower ones until the best resolution is achieved. STOP: At this point go to the in-lab worksheet and answer questions 1-3. DMM Practice – follow the techniques given above! 1. From the available loose resistors, measure the resistances and select four that have values between 300 and 6000 Ohms (no two alike). Using Table 1 on the wkst, record the color bands, in order, on each resistor starting with the band furthest from the silver or gold band and the resistance found with the DMM for each of your four unique resistors. – Page 3 of 6 – Introduction to Electricity & Circuits Physics Lab for Engineers 2. On the wkst, record the actual voltage of the 9V battery at your lab station as measured by the DMM. !Caution! Be careful to not accidentally connect, or bridge across, the two battery terminals together with plain wire or metal, this will short circuit the battery which is potentially a spark, fire, and explosion hazard. 3. Find the electrical breadboard at your table. Your instructor will explain how to work with the breadboard. Use it and some wires to mount a resistor (select any one of the four) and connect it to the battery. Also using two DMMS, place one as a voltmeter to measure the voltage across the resistor Vr and the other as an ammeter to measure current through the resistor Ir. 4. Once your circuit is setup and working Record on wkst the current and voltage. STOP: At this point go to the in-lab worksheet and answer question 4. Resistors in Series and Parallel Circuits 1. Use the variable power supply, wires and cables, and the 4 resistors to construct the circuit shown to the right on the electrical breadboard. If you need help or are unsure of your circuit construction ask for help! 2. On the wkst next to Table 2 make a diagram of the circuit and label the power supply (battery) and the resistors. 3. Using Table 2 record the values of R1, R2, R3, and R4 that you found previously with the ohmmeter. 4. Using Table 2 on the wkst record the battery voltage. 5. Measure and record the voltage across each resistor. Use Table 2 6. Measure and record the current through R1, then R2, then R3, then finally R4. Use Table 2 – Page 4 of 6 – Introduction to Electricity & Circuits Physics Lab for Engineers STOP: At this point go to the in-lab worksheet and answer questions 5-10. Tests for Linear Current-Voltage ‘Ohmic’ Relationship Plotting current vs. voltage in Georg Ohm’s model I=V/R produces a straight line with the slope equal to 1/R. From the following procedure, you will produce plots of current vs. voltage for a resistor and a light bulb. Use Excel for the plots. Power Supply: Use the Pasco Interface box as a power supply. The far right ports are signal generators which can supply an output voltage and power. Use the signal generator labelled #1. Open the Pasco Capstone software and click the “Signal Generator” icon on the left panel menu to interact with the voltage output. For this lab we only need to use the constant “DC” output. Voltage is limited to 15 volts max and current is limited to 1 amp max. The output defaults to OFF. Only turn the output ON when your circuit and all wires are completely connected; when not actively collecting data turn the voltage output OFF. !Warning! Never allow the bare wires from the Pasco output to touch each other or else you might short circuit the output and damage the interface. Remembering to keep the output turned OFF when not in active use should also help prevent this. 1. Connect the power supply, one DMM as an ammeter “mA”, and one of your resistors in a series circuit. Connect the other DMM as a voltmeter, remember to use the “COM” and “V” sockets, in parallel with the resistor. Draw a circuit diagram on the wkst and record the resistor rating from the ohmmeter test completed previously. Record the resistor color bands in order. Use Table 3 on the wkst 2. Increase the power supply voltage until a few milliamps of current is displayed on the DMM ammeter. Record the voltage and current, selecting the scale with the highest resolution. Compute the power dissipated in the resistor, 𝑃 = 𝐼𝑉, where I must be in amps, not milliamps. Use Table 3 The resistor power must not exceed 0.25 Watts to avoid overheating. The power supply voltage may not exceed 15 Volts. Vary the power supply voltage and collect 11 pairs of current and voltage readings, checking to avoid exceeding the 0.25W limit. Try to select points that more or less evenly span the range from zero to 0.25W or up to the 15V power supply limit. 3. Turn the power supply voltage back to zero. – Page 5 of 6 – Introduction to Electricity & Circuits Physics Lab for Engineers !Caution! The lightbulbs get hot quickly so do not directly touch the bulb once it is lit. The light bulb has significantly less resistance than the resistors and will draw much more current, > 250 mA. Be sure to use the 10 A socket and setting on the multimeter when measuring current through the light bulb. 4. Connect the power supply, DMM ammeter and bulb in series. Connect the DMM voltmeter in parallel with the bulb. This is the same circuit as the resistor circuit above with the bulb in place of the resistor. 5. Record 19 pairs of voltage and current readings starting at about 1/20 the maximum bulb voltage. Continue recording, increasing the voltage in steps of about 1/20 of the maximum bulb voltage. Use Table 4 on the wkst 6. Using Excel, graph the data, I vs. V, for the resistor and the bulb. Find the slope, yintercept and uncertainty on the slope for each graph. Remember you can use the Regression routine in Excel to quickly find the linear fit values and uncertainties to reasonable significant figures. See wkst Q11 STOP: At this point go to the in-lab worksheet and answer questions 12-14. Breadboard example – Page 6 of 6 – In-Lab Worksheet, Intro to Electricity PS253-Physics Lab for Engineers Name: Abdullah Alhaj Ali DMM Practice Table 1: DMM Practice. Resistor color codes and their resistances as measured by an Ohmmeter Resistor Color Code Resistance [] R1 BR BL R G .986 R2 GR BR BR G .502 R3 O BL BR G .296 R4 BR GR R G 1.491 Battery Voltage: 9.54 Resistor selected to test: R1 Resistor Current:9.6 mA Resistor Voltage: 9.47 𝑉 1. Solve Ohms law to find the current another way, using Vr and R, where 𝐼𝑐𝑎𝑙𝑐 = 𝑟⁄𝑅 . Compare |𝐼 − 𝐼𝑟 | ⁄𝐼 ) ∙ 100%. This should be less than 10%. Show Icalc and Ir by a percent difference: ( 𝑐𝑎𝑙𝑐 𝑟 your work. Resistors in Series and Parallel Circuits Draw your Circuit Diagram Table 2: DMM measurements of resistors in a simple circuit Component Resistance [ ] Power Supply –R1 .986 R2 .502 R3 .296 R4 1.491 – Page 1 of 4 – Current [ ] –6.6mA 5.4 mA 1.5 1.5 Voltage [ ] 6.77 2.69 .44 2.24 In-Lab Worksheet, Intro to Electricity PS253-Physics Lab for Engineers 2. Compute the effective resistance of R3 and R4 in parallel with R2. 3. Add R1 to the result from above to find the total resistance. Solve 𝐼𝑡𝑜𝑡𝑎𝑙 = 𝑉𝑝𝑜𝑤𝑒𝑟 ⁄𝑅𝑡𝑜𝑡𝑎𝑙 . If this result differs by more than 10% from the current measured through R1 then you must recheck all your measurements and confirm. Show your work. 4. Solve for VR1 = ItotalR1. If this result differs by more than 5% from the measured voltage across R1, then recheck all your measurements. Show your work. 5. The current through R3 and the current through R4 should be equal. If they differ by more than 5% recheck your measurements. Show your work. 6. The current through R1 is expected to equal the sum of the current through R2 and R4. If they differ by more than 10% recheck your measurements. Show your work. 7. The voltage across R2 should be equal to the sum of the voltage across R3 and R4. If they differ by more than 2% recheck your measurements. Show your work – Page 2 of 4 – In-Lab Worksheet, Intro to Electricity PS253-Physics Lab for Engineers Test for Linear Current-Voltage Relationship Draw resistor circuit diagram including DMMs. Table 3: Test of linearity for a resistor Resistor Resistance [] R1 Color Code Current [ ] 1.1mA 2.0 3.0 5.2 7.1 8.3 9.3 10.2 12.4 13.4 15.3 Voltage [ ] 1.1 1.98 2.98 5.9 6.96 8.08 9.08 9.96 12.07 13.06 14.94 Power [W] Draw light bulb circuit diagram including DMMs. Table 4: Test of linearity for a light bulb Current [ ] 46.9 56.0 62.8 70.9 78.5 85.8 94.5 100.8 107.1 113.4 118.2 123.7 128.7 134.0 150.02 153.8 158.4 167.1 184.0 – Page 3 of 4 – Voltage [ ] .9 1.35 1.71 2.17 2.63 3.09 3.67 4.13 4.6 5.06 5.42 5.88 6.34 3.80 8.29 8.64 9.10 9.99 11.82 Power [ ] In-Lab Worksheet, Intro to Electricity PS253-Physics Lab for Engineers 8. From Excel, what is the slope, y-intercept, and uncertainty on the slope for the current vs voltage graphs for the resistor and for the light bulb? 9. The slope of the resistor graph should equal 1/R where R is the value measured with the ohmmeter. a. Compute the difference between 1/R and the slope from the spreadsheet computation. 𝑑𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑐𝑒 b. Compare the difference from above to the uncertainty of the slope: 𝑢𝑛𝑐𝑒𝑟𝑡𝑎𝑖𝑛𝑡𝑦 Ideally if this graphical method successfully determines the resistance the difference will be less than twice your uncertainty. Was it successful? 10. Try to explain the shape of the bulb graph (it should be obviously non-linear), why is the slope changing, and why is the slope increasing/decreasing. Discuss any scatter of the graphed points for the light bulb. 11. Based on your work today, how well would you say Ohms law applies to real as opposed to ideal resistances? How well does it apply to a lightbulb? – Page 4 of 4 –

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