Determination of Resistances using Fixed and Variable Resistors, and Comparison of Theoretical and Measured Equivalent Resistances in Series and Parallel Combinations Brevin Kerr Candare*, Grace Petonio, Joanna Maria Sison and Alexis Teja Department of Physical Science, College of Science, University of the Philippines Baguio, Baguio City, Philippines *Corresponding author:
[email protected]
Abstract Resistance is the opposition to free flow or motion of any substance. The electric component used either to limit current through an active component or to reduce voltage in the circuit is a resistor. In this experiment, measured resistances were obtained using cylindrical ceramic resistors, potentiometer, rheostat, resistance box. The calculated percentage error for each cylindrical ceramic resistors was within the range of the tolerance – 5%. For measuring resistance using potentiometer, The closer the wiper is to the end terminal it is wired in conjunction with, the less the resistance whereas, the further away it moves from the terminal, the greater the resistance will be. Subsequently, the resistance of the rheostat is depends on the length of the resistive element or track through which the electric current is flowing. For resistance box, it was observed that the value of plugs removed is directly proportional to the resistance of the resistance box. Furthermore, the measured and theoretical equivalent resistances for each combinations were compared. Three series combinations yielded a percentage error of ____, respectively. On the other hand, the three parallel combinations obtained a ___ percentage error, respectively.
Keywords: Resistance, Equivalent Resistances, Series Circuit, Parallel Circuit, Ohms, Resistor, Resistance box
Cylindrical
ceramic
resistors,
Potentiometer,
Rheostat,
Discussion “Resistance” by definition is the opposition to free flow or motion of any substance. The electrical resistance of a material is the opposition to free flow of electrons inside that material. Electrical resistance vary with different materials and it is measured in units of Ohms [4]. A resistor is a passive electronic component that we use in electronic circuits either to limit current through an active component or to reduce voltage in the circuit (by dropping Figure 1. Resistor Electronic Symbol & voltage across the resistor). They are basically of 2 types – 1) Fixed Resistor Notation (American Standard) and 2) Variable Resistors [4]. Symbols used to represent resistors vary with different standards. Fixed resistors are the most frequently used resistors in the electronic circuits. These resistors have the fixed resistance value. Hence, it is not possible to vary the resistance of the fixed resistor. Carbon film resistors are the most widely used resistors in the electronic circuits. The carbon film resistors are made by placing the carbon film on a ceramic substrate. The carbon film acts as the resistive element to the electric current and the ceramic substrate acts as the insulating material to the electric current[5].
Figure 2. Comparison of theoretical and measured resistance of cylindrical ceramic resistors
In this experiment, five cylindrical ceramic resistors (R 1, R2, R3, R4, and R5) were used to compare the theoretical and experimental resistance. The theoretical resistance was determined through the color code chart and the experimental resistance was measured through the multimeter. Figure 2 shows the gathered data during the experiment. The theoretical resistances were 1.0 MΩ, 0.450 KΩ, 25.0 KΩ, 0.68 Ω, and 33 Ω respectively and the experimental resistances were 1.0 MΩ, 0.443 KΩ, 25.0 KΩ, 0.7 Ω, and 32.6 Ω respectively. The tolerance of each resistor was 5% making the results accurate because all the calculated percentage error is within the range of the tolerance. 1500 resistance (Ω) AB
1045 1044 1042 1042 1042 1000 718 500 370 AC BC 136.6 04.8 1 2 3 position
The device, which not only restricts the flow of electric current but also control (increase and decrease) the flow of electric current is called variable resistor. When the resistance of a variable resistor vary to a higher resistance value, the electric current flowing through the variable resistor will decrease. In the similar way, when the resistance of a variable resistor vary to a lower resistance value, the electric current flowing through the variable resistor will
.
increase[6]. The different types of variable resistors include: Potentiometer, Rheostat The potentiometer consists of three terminals among which two are fixed and one is changeable. The two fixed terminals of the potentiometer are connected to both ends of the resistive element called track and third terminal is connected to the slider or sliding wiper. The resistance of the potentiometer is changed when the wiper is moved over the resistive Figure 3. Potentiometer resistance values for each
path[6]. The resistance is lowered or increased by turning the knob clock probe and knob position or counterclockwise, where the knob direction is dependent on the end that is used with the wiper. The knob of the potentiometer was turned to different position (clockwise). As shown in Figure 3, the resistance of ports AB increases from 4.8 Ω to 1.044 KΩ. Measured resistance in BC ports decreases from 1.045 KΩ to 136.6 Ω. Lastly, resistance of AC ports were constantly measured as 1.042 KΩ. Potentiometers work by having a resistive element inside. Both end terminals are attached to it, and do not move. The wiper travels along the strip when the knob is turned. The closer the wiper is to the end terminal it is wired in conjunction with, the less the resistance, because the path of the current will be shorter. The further away it moves from the terminal, the greater the resistance will be [6]. Ports A and C yielded a constant resistance even the knob was turned because it is connected to each other making it a fixed resistor. Rheostat, adjustable resistor used in applications that require the adjustment of current or the varying of resistance in an electric circuit. Its resistance element can be a metal wire or ribbon, carbon, or a conducting liquid, depending on the application[3]. The construction of rheostat is almost similar to the potentiometer. However, in rheostat we use only two terminals for performing the operation. The resistance of the rheostat is depends on the length of the resistive element or track through which the electric current is flowing[7].
100 86.7 86.5 86.7 86.1 86.6 86.2 86 67.9 61.9 47.2 resistance (Ω) 50 40 25 AB AC19.4 BC 0.7 00.7 1 2 3 4 5 position
Figure 4 shows the measured resistance of the rheostat. Terminals B and C in the rheostat, the minimum resistance (0.7 Ω) was achieved when the wiper close was moved to the terminal B (position 5), because the length of the resistive path decreases. As a result, only a small amount of electric current is blocked and large amount of electric current is allowed. In the similar way, the maximum resistance (86.7 Ω) was achieved when the wiper was move to Figure 4. Rheostat resistance values for each probe and slider position
terminal A (position 1), because the length of the resistive path increases. As a result, a large amount of electric current is blocked and only a small amount of electric current is allowed. Same principle was observed in terminal AC but the maximum reistance was achieved in position 5 and the minimum resistance was achieved in position 1. A resistance box is a rheostat, a device meant to maintain specific electrical currents. This can be useful for testing the physical properties of electricity and for various other electrical applications. A resistance box is a typically compact piece of equipment that contains multiple resistors hooked up to one or multiple switches and is designed to provide multiple electrical resistances. The primary benefit of having a compact way to alter electrical resistance is that it removes the need to actually change resistors or unit design just to change resistance [8].
Resistance (Ω)
71 41 100 3 1.1 31 10.5 3.1 2.2 2.1 1.2 1 50 1.1 0
Labels of the plugs removed
Figure 5. Resistance reading on a resistance box for each reamoval of plug.
It was obseved that the value of plugs removed is directly proportional to the resistance of the resistance box. The initial resistance was 1.0 Ω, when plugs 30 and 40 was removed the resistance became 71.1 Ω. Resistors can be combined in two ways; series and parallel. Combination of more than one resistor is called equivalent resistor. Figure 5 shows two combinations.
Figure 5. (A) Resistors in Series, (B) Resistors in Parallel.
The first type of circuit is a series circuit (Fig. 5). In a series circuit the resistors are connected end-to-end such that the current is the same through each resistor; the current has only one path available. The voltage across each resistor depends on the resistor value[9]. For a series circuit the total equivalent resistance, R eq, is:
Req =R1 + R2 + R3 +…+ Rn
(1)
Fundamentally, a series circuit aims to have the same amount of current flow through all the components placed inline. It is called a ‘series’ because of the fact that the components are in the same single path of the current flow. For instance, when components such as resistors are put in a series circuit connection, the same current flows through these resistors, but each will have different voltages, assuming that the amount of resistance is dissimilar. The voltage of the whole circuit will be sum of the voltages in every component or resistor[10]. 1025473.28 1020000 1025000.68 Theoretical Resistance1016000 (Ω)
3 2 Combinations Measured Resistance (Ω) 1 25000.68 24950 0
200000
400000
600000
800000 1000000 1200000
Figure 6. Comparison of theoretical and measured resistance of resistors in series
Three series combinations were done in this experiment. The measured resistances were 24.95 KΩ, 1.016 M Ω, and 1.020 M Ω for combination 1 (R3 and R4), combination 2 (R1, R3 and R4), and combination 3 (R1, R2, R3, R4, and R5) respectively. Theoretical resistances were determined using eq.1 and were compared to the measured resistances. Combination 2 yielding the highest percentage error of 0.88%. The second type of circuit is a parallel circuit (Fig. 5). Resistors are said to be in parallel when they are connected at both ends, such that the potential difference applied across the combination is the same as the potential difference applied across an individual resistor. The current through each resistor depends on the resistor value. The current has more than one path available, and takes all available paths [9]. For a parallel circuit the total equivalent resistance, Req, is:
1 1 1 1 1 = + + + …+ R eq R 1 R2 R3 Rn
(2)
This circuit splits the current flow, and the current flowing through each component will ultimately combine to form the current flowing in the source. The voltages across the ends of the components are the same; the polarities are also identical[10]. 3 0.66 0.67 2 0.68 0.7 Measured 1 Combination 0.68 0.66 Theoretical 0.640.650.660.670.680.69 0.7 0.71 Resistance (Ω ) Figure 7. Comparison of theoretical and measured resistance of resistors in parallel.
For the parallel combination, three combinations were done. The measured resistances were 0.66 Ω, 0.7 Ω, and 0.66 Ω for combination 1 (R3 and R4), combination 2 (R1, R3 and R4), and combination 3 (R 1, R2, R3, R4, and R5) respectively. Theoretical resistances were determined using eq. 2 and were compared to the measured resistances. Combination 1 and 2 yielded 2.94% of error percentage. Minimal experimental errors were observed in the experiment. However possible source of some of the error were the inaccuracy of some instruments. Fluctuations in measurement using the multimeter were also observed during the experiment that contributed to the errors. Lead metals attached to the resistors were bended and scratched making the measurement inaccurate during the experiement. Conclusion
Resistor is an instrument that gives certain amount of resistance in a circuit. Four different resistors were used and observed in the experiment. Cylindrical ceramic resistor is one, in whch theoretical resistance values (indicated by color code) and the measured resistance were compared with each other. All observations were within the 5% tolerance range. Another were the Rheostat and Potentiometer. Trend of the resistance were observed as the knobs was moved/ rotated from the initial position to the final position. Same as with knob position, probe position has also great effects on the resulting resistance of both instruments. In this portion of the experiment increase, decrease and remaining of values were observed. Last is the resistance box. It was observed that the labels of the plug indicated the amount of resistance that would be added to the initial value. Resistors were also connected with one another to produce a parallel and series conformation. Theoretical total resistance was computed and was compared with the measured value. Based from the experiment, it can be inferred that different types of resistors, can be used depending on the condition to which it would be applied. One may use a fixed resistor which has a fix resistance value or a variable resistor in which one can manipulate the amount of resistance to be applied in the circuit.
[1] http://blog.delcity.net/what-does-a-resistor-do-and-why-is-it-important [2] http://www.explainthatstuff.com/resistors.html [3] https://www.britannica.com/technology/rheostat [4] http://www.circuitstoday.com/resistors-and-types-of-resistors [5] http://www.physics-and-radio-electronics.com/electronic-devices-and-circuits/passivecomponents/resistors/fixedresistor-typesoffixedresistor.html [6] http://www.physics-and-radio-electronics.com/electronic-devices-and-circuits/passivecomponents/resistors/variableresistor-typesofvariableresistor.html [7] http://www.resistorguide.com/rheostat/ [8] http://www.wisegeek.com/what-is-a-resistance-box.htm [9] http://www.phy.olemiss.edu/~thomas/weblab/215_lab_items/20_215_proce_Series_Spr2006.pdf [10] http://www.differencebetween.net/science/difference-between-series-and-parallel-circuits/
