PC1222 Fundamentals of Physics II Basic Circuits 1 Objectives Investigate the relationship among three variables (resistance, current and voltage) in direct current circuits. Investigate the behaviours of resistors in simple circuit arrangements. 2 Equipment List PASCO Circuits Experiment Boards Digital multimeter (DMM) D-cell batteries Resistors Wire leads 3 Theory 3.1 Resistance and Ohm s law When electrons, or other charge carriers, are forced to move through a medium by an applied electric field, their motion is, in most cases, retarded by scattering off imperfections (impurities) and vibrating atoms in the medium. The resistance of the movement of charged carriers is defined as R = V, I where V is the voltage, or potential difference, applied across the material and I is the current, or rate of the movement of electric charge in the material. The SI unit for resistance is volt per ampere, which is called an ohm and is represented by the Greek capital letter omega Ω. The resistance R of a medium (resistor) is dependent on its chemical properties, geometry, temperature, external magnetic field, etc. The value of resistance may also show a dependence to the magnitude and polarity of the voltage across its terminals, as is observed with a device made of semiconducting materials. Page 1 of 8
Basic Circuits Page 2 of 8 The resistance of any resistor is given by the ratio of voltage to current. For any resistor, the value of this ratio may change as the voltage and current changes. Nevertheless, the ratio of V to I defines the resistance of the resistor at that particular voltage and current. A resistor that is independent of the voltage applied across it is called an Ohmic resistor after the German physicist Georg Ohm who discovered experimentally the electrical characteristics of such a device during 1820s. Ohm s law states that the electrical current I that flows through a conductor is proportional to the potential difference V between the ends of the conductor and is inversely proportional to its resistance R. For Ohmic resistors, the quantity R is a constant for different values of V and I. Therefore, in order to show that a resistor obeys Ohm s law, it is necessary to vary the potential difference (the current I will then also vary) and observe that the ratio V/I is in fact a constant. Figure 1: Resistor colour code. The value of a resistor is typically identified on the component as a numeric value, or more commonly, by a series of coloured bands. The orientation of the bands can be determined by choosing the first band as the band closest to the end of the resistor body. The colour of the band makes up the first digit of the resistance value. For example, the resistance R of a resistor whose bands are yellow, violet, red and gold is R = yellow-violet red ± gold R = 47 10 2 Ω ± (5% of 47 10 2 Ω) R = 4700 ± 200 Ω (error rounded to one significant figure) = (4.7 ± 0.2) 10 3 Ω
Basic Circuits Page 3 of 8 3.2 Resistors in series circuits Consider the case of three resistors, R 1, R 2 and R 3, connected in series to a battery as shown in the Figure 2. In series means that the resistors are wired one after another and that a potential difference V is applied across the two ends of the series. Figure 2: Resistors in series circuit. In Figure 2, the resistors are connected one after another between a and b, and a potential difference is maintained across a and b by the battery. The potential differences that then exist across the resistors in the series produce identical currents I through them. In general, when a potential difference V is applied across resistors connected in series, the resistors have identical currents I. The sum of the potential differences across the resistors is equal to the applied potential difference V. Resistors connected in series can be replaced with an equivalent resistor R eq that has the same current I and the same total potential difference V as the actual resistors. The equivalent resistance R eq of the three resistors connected in series is given by R eq = R 1 + R 2 + R 3. The extension of n resistors connected in series is straightforward and is given by n R eq = R i. i=1 Note that when resistors are connected in series, their equivalent resistance is greater than any of the individual resistors.
Basic Circuits Page 4 of 8 3.3 Resistors in parallel circuits Consider the case of three resistors connected in parallel with a battery as shown in the Figure 3. The term in parallel means that the resistors are directly wired together on one side and directly wired together on the other side, and that a potential difference V is applied across the pair of connected sides. All three resistors then have the same potential difference V across them which produces a current through each. In general, when a potential difference V is applied across resistors connected in parallel, the resistors all have that same potential difference V. Figure 3: Resistors in parallel circuit. Resistors connected in parallel can be replaced with an equivalent resistance R eq that has the same potential difference V and the same total current I as the actual resistors. The equivalent resistance of the three resistors connected in parallel is given by 1 R eq = 1 R 1 + 1 R 2 + 1 R 3 In general, the equivalent resistance for n resistors connected in parallel is given by 1 R eq = Note that when two or more resistors are connected in parallel, the equivalence resistance is smaller than any of the combining resistances. n i=1 1 R i.
Basic Circuits Page 5 of 8 4 Laboratory Work Part A: Ohm s Law and Resistances In this part of the experiment, we will investigate the three variables, resistance R, potential difference V and current I, involved in a mathematical relationship known as Ohm s law. Figure 4: DMM in circuit to measure current through resistor. Figure 5: DMM in circuit to measure voltage across resistor. A-1. Choose one of the resistors you have been given. Record its colour codes in Data Table 1. Use DMM to measure the resistance of the resistor and record it as R in Data Table 1. A-2. Measuring current. Construct the circuit shown in Figure 4 by pressing the leads of the resistor into two of the springs in the experimental section on the circuits experiment board. A-3. Connect the circuit and read the current that is flowing through the resistor. Record this value as I in Data Table 1. A-4. Remove the resistor and choose another. Record its resistance value as R in Data Table 1 then measure and record the currents as in steps A-2 and A-3. Repeat the process until you have TEN sets of data. A-5. Measuring voltage. Disconnect the DMM and connect a wire from the positive lead (spring) of the battery directly to the first resistor you used as shown in Figure 5. Measure the voltage across the resistor and record it as V in Data Table 1. A-6. Remove the resistor and choose the next one you used in step A-4. Record its voltage in Data Table 1 as in step A-5. Repeat the process until you have completed all of the resistors used in step A-4.
Basic Circuits Page 6 of 8 Part B: Series Circuit In this part of the experiment, we will investigate the behaviours of resistors in a series circuit. B-1. Choose THREE unequal resistors that you have been given. We will refer to one as #1, another as #2 and the third as #3. Use the DMM to measure the resistance of each of your three resistors. Enter these values as R 1, R 2 and R 3 respectively in Data Table 2. Figure 6: Resistors in a series circuit. B-2. Now connect the three resistors into the SERIES CIRCUIT as in Figure 6, using the spring clips on the circuits experiment board to hold the leads of the resistors together without bending them. B-3. Measure and record the resistances of the combinations R 12, R 23 and R 123 by connecting the leads of the DMM between the points at the ends of the arrows. Record your readings in Data Table 2. Figure 7: Voltages in series circuit. B-4. Now connect two wires to the D-cell to the resistor combination as in Figure 7. B-5. Use the voltage function on the DMM to measure the potential differences across the individual resistors ( V 1, V 2 and V 3 ) and then across the combinations of resistors ( V 12, V 23 and V 123 ). Record your readings in Data Table 2.
Basic Circuits Page 7 of 8 Figure 8: Currents in series circuit. B-6. Now change the leads in your DMM so that they can be used to measure current. In order to measure current, the circuit must be interrupted and the current allowed to flow through the meter. Disconnect the lead wire from the positive terminal of the battery and connect it to the red (+) lead of the meter. Connect the black (-) lead to R 1, where the wire originally was connected. Record your reading in Data Table 2 as I 0. B-7. Move the DMM to the positions indicated in Figure 8, each time interrupting the circuit and carefully measuring the current in each one. Record your readings in Data Table 2. Part C: Parallel Circuit In this part of the experiment, we will investigate the behaviours of resistors in a parallel circuit. C-1. Choose THREE unequal resistors that you have been given. We will refer to one as a, another as b and the third as c. Use the DMM to measure the resistance of each of your three resistors. Enter these values as R a, R b and R c respectively in Data Table 3. Figure 9: Voltages in parallel circuit. Currents in parallel cir- Figure 10: cuit. C-2. Construct a PARALLEL CIRCUIT using all three resistors as in Figure 9. Measure and record the resistances of the combination R abc in Data Table 3.
Basic Circuits Page 8 of 8 C-3. Use the voltage function on the DMM to measure the potential differences across the individual resistors ( V a, V b and V c ) and then across the combination of resistors ( V abc ). Record your readings in Data Table 3. C-4. Connect the parallel circuit as in Figure 10 using all three resistors. Review the instruction for connecting the DMM as an ammeter. Connect it first between the positive terminal of the battery and the parallel circuit junction to measure I 0. Then interrupt the various branches of the parallel circuit and measure the individual branch currents. Record your measurements in Data Table 3. Part D: Combination Circuit In this part of the experiment, we will investigate the behaviours of resistors in a simple combination circuit. D-1. Choose THREE unequal resistors that you have been given. We will refer to one as A, another as B and the third as C. Use the DMM to measure the resistance of each of your three resistors. Enter these values as R A, R B and R C respectively in Data Table 4. Figure 11: Resistors in a combination circuit. D-2. Connect the COMBINATION CIRCUIT as in Figure 11. Measure and record the various combinations of resistance R BC and R ABC in Data Table 4. D-3. Use the voltage function on the DMM to measure the potential differences across the individual resistors ( V A, V B and V C ) and then across the combinations of resistors ( V BC and V ABC ). Record your readings in Data Table 4. D-4. Change the leads in your DMM so that they can be used to measure current. Connect it first between the positive terminal of the battery and the resistor R A to measure I 0. Then interrupt the resistor R A and the parallel circuit junction to measure I A. Interrupt the various branches of the parallel circuit and measure the individual branch currents, i.e. I B and I C. Lastly connect it between the negative terminal of the battery and the parallel circuit junction to measure I 4. Record your measurements in Data Table 4. Last updated: Sunday 17 th August, 2008 4:04pm (KHCM)