# 3 DC Circuits, Ohm's Law and Multimeters

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1 3 DC Circuits, Ohm's Law and Multimeters Theory: Today's lab will look at some basics of electricity and how these relate to simple circuit diagrams. Three basic terms are important to a study of electricity. They are basic to understanding Ohm's Law which is Voltage = Current constant This constant is defined as the resistance of an object. Its unit is the ohm or Ω. Current is defined as the flow of electrical charge from one place to another. It is the amount of charge which passes a given point in a unit of time and is measured in units of amperes (amps = coul/sec). Voltage is a measure of potential (potential difference) between two points in a conductor. It is a measure of the amount of energy it takes to move charge from the one point to the other. It is measured in units called volts (volt = Joule/coulomb). Resistance is a measure of the amount of impedance a material presents to the flow of electricity. George Ohm showed it is the ratio of the voltage across a material to the current that can then flow through it. It depends upon the properties of the conducting material (its nature and dimensions) but for metallic conductors is usually a constant at constant temperature. It is measured in units of ohms, where one ohm is defined as 1 volt/ 1 ampere. We will demonstrate Ohm's Law for several combinations of resistors, verifying the general rule V R eq = I 1 ' 1 \$ where R eq =! Ri for resistors combined in series, and =! % " R eq & R i # combined in parallel. Apparatus: for resistors Three new items that this lab uses are resistors, multimeters and power supplies. Resistors are used in large numbers in electronic equipment to control the flow of electrical current. Physically, they are manufactured in a number of styles which 1

2 feature either high power capacity, high precision, or low cost. This lab will use the most common, low cost, carbon composite style shown in Figure 3.1. The physical size determines the power rating ( P = IV = I 2 R = V 2 /R ). The ¼ watt (W) size is about 7mm long by 2 to 3mm in diameter, while the ½ W, 1W, and 2W are progressively larger. The 1/4W resistors are designed to handle up to 1/4W of power before overheating. The low voltage in this experiment make it safe to feel the resistor in use to check if it is overheating. If it becomes hot (rather than just warm) reduce the voltage or choose a larger resistance value resistor. A quick calculation will also serve to check the power, before the circuit is energized. If a resistor should ever become smoking hot, discard it since it will probably be damaged. Figure 3.1: Colored bands indicate the resistance of the resistor. The resistance value of a resistor is determined during manufacture by the composition of the carbon mix it is made from. This resistance is marked on the resistor, usually by colored bands as shown in Figure 3.1. As shown, the color bands usually butt up against one end of the resistor shell. To read these, begin with the band closest that end and decode it and the second band using the following table: Table 3.1: Color Code Resistor Bands 0 black 5 green 1 brown 6 blue 2 red 7 violet 3 orange 8 gray 4 yellow 9 white The third band, when similarly decoded, is the power of ten of the multiplier. For example, a resistor marked brown, black, red should have a resistance of 10 x 10 2 which equals 1000Ω or 1 kω. Note that there is no decimal point between the 1 and 0. The fourth band marks the precision (brown or no mark is ± 20%. silver is ± 10%, gold is ± 5%) and indicates how much the actual resistance can differ from that indicated by the colored bands. A fifth band sometimes indicates reliability. Commercial resistors are designed to have an almost constant resistance over the range of currents and voltages within the power rating. Thus a current versus voltage plot will be a straight line within 2

3 parts per million. Other devices are not so linear, such as light bulbs, diodes, or LED's which have resistances which vary with current and voltage. The Multimeter: In this laboratory you will make use of a multimeter (Wavetek DM28XT), shown in the figure to the right, to measure voltage, current, frequency capacitance, and resistance. This particular meter has the features typically found in many multimeters today. We have already used the DC voltmeter function in the electric field experiment. Each button, switch and connector has a somewhat cryptic label that provides the experienced user with important clues as to how to use the meter. It is important when using such a meter to understand what you are measuring and how to use the meter. This is important for your safety, the protection of the meter and the accuracy of your measurements. The rotary switch in the center determines what is measured and also sets the range of values to be measured. For example, if you wish to measure electrical current that you expect to be about 1.5 ma, you would set the rotary switch to the "2m" position within the A region. This tells the meter that you expect a current that is less than 2 ma. The result of the measurement is shown in the display and ma in the display indicates that the quantity shown is ma and not A. If the actual current is greater than 2 ma then the meter will display OL indicating an overload. You will then have to raise the range to 20 ma in order to get a reading. When the switch is set to 20 ma you will notice that you lose one significant digit of accuracy in the reading. There are four different input plugs, which receive cables (often called probes) that are connected to the circuit. All measurements make use of the COM (common) input. For voltage, frequency and resistance measurements the leftmost plug labeled V-Ω is used along with COM. For low currents and capacitance the plug labeled ma Cx is used along with COM. For currents up to 10 A the 10 A plug is used along with COM. Just below the display are four buttons. The function of the ON/OFF and DC/AC are very important but self-explanatory. The hold button will "hold" the display at the current value until it is pressed a second time. The MAX button causes the display to show the maximum value of the quantity being measured until it is pressed again. It should be noted that AC readings are root-mean-square (RMS) values. The accuracy of the multimeter is specified for each type of measurement in the sections that follow. This accuracy is expressed as a percentage plus a factor related to the number of digits in the display. For example, DC voltages have an uncertainty of 3

4 0.5% plus one least significant digit. In the 2 V range, the least significant digit is ± V. So if you were measuring a voltage of 1.0 V, the 0.5% would give an uncertainty of V and you would add the least significant digit to give an overall uncertainty of ± V. Voltage Measurements To make a voltage measurement, select AC or DC, turn the rotary switch to the V area and select the appropriate range. If you are unsure of the range, set the rotary switch to the highest range and then lower it later. Insert the probes into the V Ω and COM plugs and then connect them to the appropriate points in the circuit. If you are making a DC measurement then the V Ω probe should be connected to the most positive voltage and the COM probe should be connected to the most negative. If the probes are not connected correctly, then the display will indicate a negative voltage, but there is no need to switch the connections. If you are making an AC voltage measurement, the COM probe should be connected to the point closest to ground. Electrical Specifications for voltage measurements DC VOLTS Input Impedance 200mV, 2V, 20V, 200V, 1000V ± 0.5% + 1 lsd* 10 MΩ 200mV Range 500/350VRMS 15sec; All other ranges 1000VDC/750VRMS AC VOLTS Input Impedance * lsd =least significant digit 200mV, 2V, 20V, 200V, 750V Hz Range - ± 1.0% + 4 lsd* Hz Range - ± 1.5% + 4 lsd* 10 MΩ 200mV Range 500VDC/350VRMS 15sec; All other ranges 1000VDC/750VRMS 4

5 Current Measurements To make a current measurement, select AC or DC and turn the rotary switch to the A area and select the appropriate range. If you are unsure of the range, set the rotary switch to the highest range and then lower it later. Insert the probes into the ma C x and COM plugs and then connect them to the circuit. It is important to note that the current meter must be part of the circuit as shown in Figure 3.3, which shows a typical use of voltage and current meter. (If you expect a current in the 10 A range, then the 10 A and COM plugs should be used and the rotary switch should be set to the 20m/10A position.) If you are making a DC measurement then the ma C x probe should be connected to the most positive voltage and the COM probe should be connected to the most negative voltage. If the probes are not connected correctly, then the display will indicate a negative current, but there is no need to switch the connections. If you are making an AC voltage measurement, the COM probe should be connected to the point closest to ground. Electrical Specifications for current measurements DC Current 200µA, to 200mA range 10A range Input Protection 200µA, 2mA, 20mA, 200mA, 10A ± 1% + 1 lsd* ± 2% + 3 lsd* Fast acting ceramic fuse: 500mA on ma input 20A/600V on 10A input AC Current 200µA, to 200mA range 10A range Input Protection *lsd =least significant digit 200µA, 2mA, 20mA, 200mA, 10A ± 1.5% + 4 lsd* (50-500Hz) ± 2.5% + 4 lsd* (50-500Hz) Fast acting ceramic fuse: 500mA on ma input 20A on 10A input 5

6 Resistance Measurements The multimeter can also be use to measure the resistance of a resistor or other circuit component. In making resistance measurements the resistor must be completely removed from the circuit. The V Ω probe should be connected to one end of the resistor and the COM probe should be connected to the other end. Turn the rotary switch to the Ω area and select the appropriate range. Resistance 200Ω to 2MΩ range 20MΩ range 2000MΩ range * lsd =least significant digit 200Ω, 2kΩ, 20kΩ, 200kΩ, 2MΩ, 20MΩ, 2000MΩ ± 1% + 4 lsd* ± 2% + 5 lsd* ± 5% + 10 lsd* 500VDC/AC RMS Capacitance Measurements The multimeter can also be use to measure the capacitance of a capacitor. In making capacitance measurements the capacitor must be completely removed from the circuit. The ma C x probe should be connected to one end of the capacitor and the COM probe should be connected to the other end. Turn the rotary switch to the F (farad) area and select the appropriate range. Capacitance All ranges 2 nf, 200 nf, 2 µf, 20 µf, 200 µf, 2 mf, 20 mf ± 3.% + 4 lsd* *lsd =least significant digit F0.5A/250V fast acting ceramic fuse Experiment: DC Circuits 1. Use the multimeter to measure the actual resistances of a nominal 5.1 kω and a 10kΩ resistor separately. Then connect them in series and measure the total series resistance. Compare with theory using experimental uncertainties. Repeat with the resistors in parallel. 6

7 Figure 3.3: Series Circuit 2. Use the multimeter to measure the actual capacitance of a nominal µf and a µf capacitor separately. Please note that some capacitors are polarized, which means that the plus side of the capacitor must be connected to the ma C x input of the multimeter. Then connect them in series and measure the total series capacitance. Compare with theory using experimental uncertainties. Repeat with the capacitors in parallel. Note: polarized capacitors are subject to student damage and are not recommended for this experiment. Capacitors of values less than 0.2 µf are usually not of the polarized variety. 3. Wire up the series circuit shown in Figure 3.3 consisting of a power supply, a resistor, and two multimeters, one as a voltmeter and one as an ammeter. Make measurements for power supply settings from 0 to 10 volts at each, recording the readings on both meters. Use the spreadsheet to graph the current versus voltage. From the slope of the graph determine the resistance of the resistor. Compare this value with its experimental uncertainties to its nominal value (see its color-codes) and to the value you obtain using one multimeter as an ohmmeter. 4. Now, add a 5.1 kω resistor in series with the 10 kω already in place. Measure the voltage across each resistor and the current through each resistor. Compare with theory. In your report, sketch the circuit (as a circuit diagram similar to Fig 3.3) and the placement of the meters in the circuit. 5. Move the 5.1 kω resistor to be in parallel the 10 kω resistor. Measure the voltage across each resistor and the current through each resistor. Compare with theory. Sketch this circuit showing the meters. 7

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