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Experiment 3
SERIES RESISTIVE AND PARALLEL RESISTIVE CIRCUITS
At the end of this experiment, the student should be able to: TLO 1: Identify series circuits. TLO 2: Calculate and measure the resistance of a series circuit. TLO 3: Measure the current flow in a series circuit using an ammeter. TLO 4: Measure the voltage drops in a series circuit using a voltmeter. TLO 5: Identify parallel circuits. TLO 6: Calculate and measure the resistance of a parallel circuit. TLO 7: Measure the current flow in a parallel circuit, and measure the voltage across parallel resistors. TLO 8: Determine that a parallel circuit has more than one path for current flow, using an ammeter and miniature lamps. INTRODUCTION: Resistance in a circuit may or may not be desirable. For example, the wire used to connect components in a circuit has a small amount of resistance. Power is dissipated in the wire resistance and is thus lost because it performs no useful work. Copper wire is a relatively good conductor and is used in most circuits to lower power losses. On the other hand, it may be necessary to put a certain amount of resistance into a circuit to limit the current or to produce a certain drop in voltage. The power dissipated by the resistor would be lost, but would be a “necessary evil” in this case because the circuit required it. A desirable power loss occurs in a resistance when useful work is done, such as heating the filament of lamp. A series circuit is the simplest form of all circuit. All the components of the circuit are connected “end to-end” to form a single path. Refer to Fig. 3 – 1.
- I I (^) I I R R R BT Fig. 3 – 1 Circuit current (I) supplied by the voltage source BT has only one path to take in flowing from the positive terminal to the negative terminal, and that is through each
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successive component of the series circuit. Thus, in a series resistive circuit, the sum of the resistances determine the total amount of circuit current. A parallel circuit may be thought of as being formed by connecting two or more components “side – by – side”, or input – to – input and output – to – output. For example, when you measure the voltage drop across a resistor the internal resistance of the voltmeter is in parallel with the resistor. Resistors or other components may be connected to form as many parallel “branches” as desired. There are two basic differences between parallel and series circuits. Refer to Fig. 3 – 2. First, the same source voltage is applied across all branches of the circuit simultaneously. Second, each branch of the circuit acts as a separate circuit, and thus there is more than one path for the current to follow. Therefore the total circuit current is equal to the sum of the branch currents.
BT (^) EBT R R I (^1) R1 R IT IT I 2 I 3 EBT EBT BRANCH 1 BRANCH 2 BRANCH 3 Fig. 3 – 2 The concept of resistances in parallel is easily understood if you think of the resistors as conductors of current. If one resistor is connected to a power source, there is one path for current flow. If another resistor is connected in parallel with the first, two current paths are created and more current can flow. Each additional parallel resistor creates another path and, as more parallel resistors are added, more current flows. If more current flows, it is evident that less total resistance is offered to the power source to limit the flow of current. From this you can conclude that the total resistance of resistors in parallel must be less than any one of the resistors considered separately. In fact, the total resistance is less than the lowest value resistor in the circuit. The ability of a resistor to conduct current is referred to as conductance (G) and is measured Siemens (S) or mhos. Conductance is the inverse, or reciprocal, of resistance. This is expressed mathematically as 𝐶𝑜𝑛𝑑𝑢𝑐𝑡𝑎𝑛𝑐𝑒 = 1 /𝑅 The more resistors you add in parallel the more conduction paths you create. The conductance effects can be added directly. This is expressed as follows: 𝑇𝑜𝑡𝑎𝑙 𝐶𝑜𝑛𝑑𝑢𝑐𝑡𝑎𝑛𝑐𝑒 = 𝐺𝑇 = 𝐺 1 + 𝐺 2 + 𝐺 3 +. ..
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R5 - 3.3 kΩ, 1 W S1 - SPST, Component Board M Universal Experiment Board K
PROCEDURES:
Note: In the absence of an actual laboratory set-up, you may answer the module based on the concepts learned from the lecture subjects. As a verification, perform a simulation with your simulator of choice. For every circuit, attach a screenshot of the set-up in your report. Examples of simulators: LTspice (Free), Electronic Workbench, Circuit Construction Kit: DC at phet.colorado.edu TLO 1: Identify series circuits.
- Examine the four circuits shown in Fig. 3 – 3. Circle the identifying numbers of the series circuits. (1) (^) (2) (3) (4) Fig. 3 – 3 TLO 2: Calculate and measure the resistance of a series circuit.
- Record in the Table 3 – 1, the color code, indicated value and tolerance of resistors R1 through R4.
- Use the Electronic VOM (ohmmeter function) to measure the value of each resistor. Enter the measured values in Table 3 – 1.
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RESISTOR
COLOR CODE
(COLORS)
INDICATED
VALUE
TOLERANCE
MEASURED
VALUE
R1 5 % 998
R2 10 % 995
R3 20 % 1465
R4 5 % 1480
Table 3 – 1
- Adding the indicated values together, calculate total resistance, RT(indicated). RT(indicated) = ___________________________ = __________ Ω
- Adding the measured values together, calculate total resistance, RT(measured). RT(measured) = ____________________________ = __________ Ω_ Is the total indicated resistance value RT (indicated) the same as the total measured value RT (measured)? __________
- Connect resistors R1 through R4 in a series in Fig. 3 – 4.
- Measure the total circuit resistance RT with the ohmmeter. RT(circuit) = 4,878 Ω Does the total circuit resistance value, RT (circuit) agree with the results in TLO 2: 3 and 4)? __________ Allowing error factors mentioned in TLO 2 - 5 the results should be in agreement. Thus verifying that the formula for the total resistance in a series circuit is 𝑅𝑇 = 𝑅 1 + 𝑅 2 + 𝑅 3 + …
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RT(calculated) = ___________________________ = __________ Ω Does the total calculated circuit resistance value RT(calculated) agree with the result of TLO 2 – 6 __________ List the possible factors that could account for the results not being in perfect agreement.
- Now measure the current at different locations throughout the series circuit. Connect the milliammeter between R1 and R2 as shown in Fig. 4 – 6. mA R 1K R 1.5K R 1K R 1.5K
0 – 25Vdc 0 – 10mAdc Fig. 3 – 6
- Adjust the power source to 25Vdc.
- Measure and record the current flowing between R1 and R2. IR1 – R2 = 4.95 mAdc
- Return the voltage to zero.
- Repeat TLO 3 – 8 with the milliammeter connected, in turn, to the following circuit positions: IR 2 – R 3 = 4.90 mAdc IR3 – R4 = 4.85 mAdc IR4 – R5 = 5.01 mAdc Compare the current values at the different locations. Are they the same? _________
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What important rule of the series circuit have you verified?
TLO 4: Measure the voltage drops in a series circuit using a voltmeter.
- Connect lamp DS1, in a series with the ammeter and switch S1, across the dc power source as shown in Fig. 3 – 7. Do not connect VOM at this time. A V
S
- (^) - 0 – 1Adc DS 5Vdc ELECTRONIC VOM Fig. 3 – 7
- Set the ammeter to the 1 Adc range.
- Close switch S1.
- Adjust the power source to 5Vdc and observe the brilliance of lamp DS1.
- Measure the current through lamp DS1. IDS1 = 0.29 Adc
- Use the electronic VOM (5Vdc range) to measure the voltage drop across lamp DS1 as shown in Fig. 3 – 7. (The voltage measured across lamp DS1 is also called the voltage drop across lamp DS1). EDS1 = 4.82 Vdc
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- Enter the current, I, and voltages EDS1 and EDS2 in Table 3 – 2.
- Open switch S1.
- Connect lamp DS3 into the circuit in series with DS1 and DS2.
- Close switch S1 and note the brightness of the lamps.
- Measure the current flowing through the circuit. I = 0.88 Adc
- Measure the voltage across each of the lamps. EDS1 = 1.62 Vdc EDS2 = 1. 72 Vdc EDS3 = 1.65 Vdc
- Enter the circuit, I, and voltages EDS1, EDS2, EDS3, in Table 3 – 2.
- Open switch S1.
- Connect lamp DS4 into the circuit in series with DS1, DS2 and DS3.
- Close switch S1 and note the brightness of the lamps.
- Measure the current flowing through the circuit. I = 1.16 Adc
- Measure the voltage across each of the lamps. EDS1 = 1.28 Vdc EDS2 = 1.31 Vdc EDS3 = 1.25 Vdc EDS4 = 1.36 Vdc
- Enter the circuit current, I, and voltages EDS1, EDS2, EDS3 and EDS4 in Table 3 – 2.
- Open switch S1. Refer to Table 3 – 2. Did the circuit current decrease as lamps were added to the series circuit?
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Did the voltage drops across individual lamps decrease each time a lamp was added in series? __________ Do the sum of the voltage drops equal the source voltage? ________ TLO 5: Identify parallel circuits.
- Examine the four circuits shown in Fig. 3 – 9. Circle the identifying numbers of the parallel circuits. (1) (2) (3) (4) Fig. 3 – 9 TLO 6: Calculate and measure the resistance of a parallel circuit.
- Calculate the total resistance of resistors R 3 and R 4 in parallel. RT = _________________________________ = __________ Ω
- Connect resistors R 3 and R 4 in parallel as shown in Fig. 3 – 10. Do not connect resistor R 5 at this time!
- Set the Electronic VOM to the ohmmeter function and measure the parallel resistors R 3 and R 4. RT = 742 Ω
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mA R 1.5K R 1.5K R 3.3K
0 – 100mAdc 0 – 30Vdc Fig. 3 – 11
- List the total parallel resistance RT of resistor R 3 and R 4 as calculated in TLO 6- 1 , measured with the ohmmeter in TLO 6-3, and calculated by Ohm’s Law in TLO 7-
- RT(calculated) = _______________ Ω RT(ohmmeter) = _______________ Ω RT(Ohm’s Law) = _______________ Ω Are the three total resistance values approximately the same?______ What factors, besides resistor tolerance, would contribute to variation among the three values of RT?
- Connect resistor R 5 into the circuit in parallel with resistors R 3 and R 4 as shown in Fig. 3 – 11.
- Adjust the power source to 30Vdc.
- Measure the total current flow IT in the circuit. IT = 48.3 mAdc
- Measure the voltage drop across each individual resistor using the Electronic VOM. ER 3 = 28.93 Vdc ER 4 = 29.25 Vdc ER3 = 28.65 Vdc
- Return the voltage to zero.
- Calculate the total resistance RT in the circuit using Ohm’s Law for resistance. RT = _________________________________= __________ Ω
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- List the total parallel resistance RT of the resistors R 3 , R 4 and R 5 as calculated in TLO 6 - 4, measured with the ohmmeter in TLO 6-6, and calculated by Ohm’s Law in TLO 7 - 12. RT(calculated) = _______________ Ω RT(ohmmeter) = _______________ Ω RT(Ohm’s Law) = _______________ Ω Are the three total resistance values approximately the same? ______ TLO 8: Determine that a parallel circuit has more than one path for current flow, using an ammeter and miniature lamps.
- Connect lamp DS1, in series with the ammeter and switch S1, across the dc power source as shown in Fig. 3 – 12.
- Close switch S1.
- Adjust the power source of 6.3Vdc and note the brightness of lamp DS1.
- Measure the total circuit current. IT = 0.24 Adc
- Open switch S1 and connect lamp DS2 in parallel with lamp DS1 as shown in Fig. 3 – 12. A S
- (^) - 0 – 1Adc 6.3Vdc DS1 DS2 DS3 DS Fig. 3 – 12
- Close switch S1 and note the brightness of lamps DS1 and DS2. Is there any change in brightness from TLO 8:3?__________
- Measure the total circuit current. IT = 0.48 Adc
- Open S1 and connect lamp DS3 in parallel with DS1 and DS2 shown in Fig. 3 – 12.
