EMF, Terminal Voltage, and Internal Resistance Mary Grace DC. Odiamar De La Salle University University 2401 Taft Avenue, Malate, Manila, Philippines
[email protected] Abstract – This paper is generally about the inspection and
examination of voltage sources of direct-current circuits, known otherwise as seats of emf or emf devices. The experiment aimed to illustrate the difference between emf and terminal voltage, to show how an ideal battery is different from a real one with an internal resistance, to measure the electromotive force of a battery, to calculate the internal resistance of a real battery and to show the variants of a battery’s terminal voltage with its current output through experimentation. In this experiment, the internal resistance of Daniell cell (wet cell) was computed by measuring the voltage across the circuit where the values of resistances R were given; current I and internal resistance r were then computed through Ohm’s Law and through the equation of terminal voltage of a real battery, respectively. On the other hand, the carbon battery’s internal resistance was c omputed by measuring the voltage across the circuit where the values of current were given; internal resistance r was also computed through the equation of terminal voltage of a real battery. The acquired results were very likely to show how a battery’s voltage vo ltage is related to current and resistance, as well as how to calculate a battery’s internal resistance. – – Emf, Emf, Terminal Voltage, Internal Resistance, Battery, Keywords Daniell Cell, Dry Cell, Voltmeter, Ammeter, Rheostat
I. I NTRODUCTION Electric circuits are essential means to transport electric potential energy from one region to another. When charged particles move within a circuit, energy is transported from a source such as a battery to an instrument where the said energy is stored or transformed into other form/s. Generally, today’s modern world is heavily dependent on electric circuits. They have been used for years because of their effectiveness and practicality – practicality – they they typically allow energy to be conveyed without moving any parts. One should note that electric circuits are at the heart of every electronic device. Every electric circuit consists of components, and these often include sources, resistors, and other circuit elements interconnected in a network [1]. One element to be noted in this paper is the source of the circuit, more often known as the battery. In a battery, a chemical reaction occurs when a load completes the circuit between the terminals. The chemical reaction then transfers electrons from one terminal to another terminal. The electric potential difference is caused by the positive and negative charges on the battery terminals. The maximum potential difference of a battery is called the electromotive force or emf, designated by Ɛ [2].
II. THEORETICAL BACKGROUND A. Seats of EMF and EMF When a potential difference or voltage is applied across a circuit, current will be allowed to flow. These devices that are responsible for the flow of charge in circuits are called seats of emf, emf devices or simply voltage sources. The emf is not really a force but is the work per unit charge that an emf device does in moving positive charges from lower potential terminal (-) to higher potential terminal (+). Its unit is joule per coulomb or volts. A voltage source i s labeled with its emf value, Ɛ, which is equivalent to Ɛ =
[3].
B. Emf, Terminal Voltage, Voltage, and Internal Resistance A real battery is made of matter; therefore, there is resistance r to the flow of charge inside the battery. This resistance inside the battery is called internal resistance r. An ideal battery with zero internal resistance has a terminal voltage equal to its emf, no matter how much current is drawn from them. However, a real battery in a circuit where current is drawn from has a terminal voltage which is not equivalent to its emf [4]. Its terminal voltage is given by b = ε – . In this equation we notice that the terminal voltage drops as we draw more current from the battery because of the internal resistance. In rearranging the equation, we can get a battery’s internal resistance by r =
C. Daniell Cell and Dry Cell Cell John Frederick Daniell, a chemistry professor in London, has developed an emf device that supplied constant electric current. The Daniell cell is a type of wet cell and has also been called as a gravity cell and crowfoot cell. In the early 1800s, the cell became a popular power supply in the laboratories and in the telecommunications industry. The cell is made of copper and zinc electrodes and an electrolyte solution. This battery converts chemical energy to electrical energy whenever a load is present. Nowadays, better batteries with low internal resistances have been developed. Cars consume lead-acid batteries, which is also a wet cell. This battery comprises of lead and lead oxide electrodes and an electrolyte solution. In contrast to the batteries of the earlier centuries, modern batteries have been constructed to be very portable and
maintenance-free. One of today’s primary batteries is the zinccarbon battery, a dry cell, and also known as the standard carbon battery. It is a very cheap battery and comes in various sizes – AA, AAA, C and D [3].
III. METHODOLOGY
slider of the rheostat was adjusted until the ammeter reads 0.05 amperes. The experiment was repeated with different values of the current. The rheostat was adjusted with the following readings in the ammeter – 0.10, 0.15, 0.20 and 0.25 amperes. The measured voltages were logged. Internal resistance r was then computed through the equation r =
.
A. Preliminary Steps Before starting the experiment, the wires should be checked for continuity as for the research to have fewer errors and to yield more accurate results. The functionality of these wires could be checked by just connecting the probes of the voltmeter-ohmmeter-milliammeter (VOM) to the ends of the wires. The VOM should be set to the ohmmeter function. The batteries to be used in the experiment should be guaranteed to be new and working as well. B. Daniell Cell (Wet Cell) To perform the experiment for the Daniell cell, the Figure 2. Setup for dry cell [3]. voltage across the terminals of the Daniell cell was first measured with a voltmeter. The value obtained is equal to its IV.R ESULTS AND DISCUSSION emf. A series circuit involving a Daniell cell, a decade resistance box set to 20 Ω and a voltmeter connected to the circuit in parallel was then constructed. The first reading in A. Daniell Cell (Wet Cell) 1) First Trial: the voltmeter was recorded. The experiment was repeated Ɛ = 1.1 volts with different values of the decade resistance box – 40, 60, 80 and 100 Ω. The measured voltage values were then recorded. TABLE 1 Internal resistance r was computed through the equation r MEASUREMENTS =
. This experiment had two trials. R (Ω) 20 40 60 80 100
Figure 1. Setup for Daniell Cell [3].
C.
Carbon Battery (Dry Cell)
For the dry cell, the voltage across the terminals of this battery was measured first as well. The value obtained was recorded as its emf. A series circuit was constructed as well, with the voltmeter connected across the battery in parallel. It should also be noted that one end terminal and the center tap of the rheostat is connected, while the other end terminal of the rheostat is disconnected. In getting the voltage reading, the
Measured Vab (Volts) 0.26 0.41 0.52 0.60 0.66
I (A) 0.013 0.0103 0.00867 0.00750 0.00660
Calculated r (Ω) 64.62 66.99 66.90 66.67 66.67 Average r = 66.37 Ω
0.7 0.6 ) 0.5 s t l o0.4 v ( b0.3 a V0.2 0.1 0 0
0.005
0.01 I (A)
Figure 3. Vab vs. I (First trial for Daniell cell)
0.015
Current I was calculated from the measured voltages and
resistances by Ohm’s Law, I = . With the complete data, the
internal resistances r were calculated through the equation r =
which was derived earlier. It should be noted from the
data that as the external resistance increases, the current decreases. The internal resistance increases together with the external resistance and the average internal resistance obtained for trial one is 107.54 Ω. In the graph, the slope determines the internal resistance r. It was computed through
data that as the external resistance increases, the current m = . In this trial, m= ; m = -100. The decreases. The internal resistance increases together with the negative sign in the slope indicates an inverse relationship external resistance and the average internal resistance between the terminal voltage and the current. The internal obtained for trial one is 66.37 Ω. In the graph, the slope resistance from slope is equal to 100 Ω, a value which is very determines the internal resistance r. It was computed through close to the average r, which is 107.54 Ω. The value of emf Ɛ m = . In this trial, m= ; m = -67.86. The can also be obtained from the graph through the equation y = negative sign in the slope indicates an inverse relationship mx + b. Y-intercept b is equal to the emf Ɛ. Getting emf Ɛ, between the terminal voltage and the current. The internal 0.39 = (-100)(6.5x10-3) + b. The equation yielded b = 1.04, a resistance from slope is equal to 67.86 Ω, a value which is value equivalent to the measured emf 1.08 V. It is noted that very close to the average r, which is 66.37 Ω. The value of the first and second trials have precise results. emf Ɛ can also be obtained from the graph through the equation y = mx + b. Y-intercept b is equal to the emf Ɛ. Getting emf Ɛ, 0.52 = (-67.86)(8.67 x10-3) + b. The equation B. Carbon Zinc (Dry Cell) Ɛ = 1.08 volts yielded b = 1.11, a value equivalent to the measured emf 1.10 TABLE 3 V. MEASUREMENTS
2)
Second Trial: Ɛ = 1.08 volts
I (A) 0.07 0.10 0.15 0.20 0.25
TABLE 2 MEASUREMENTS
R (Ω)
Measured Vab (Volts) 0.17 0.29 0.39 0.46 0.52
20 40 60 80 100
I (A) 0.0085 0.00753 0.00650 0.00575 0.00520
Measured Vab (Volts) 2.37 2.25 2.05 1.85 1.65
Calculated r (Ω) 107.06 108.97 106.15 107.83 107.69 Average r = 107.54 Ω
0.6 0.5
2.5 2
) s t l o1.5 v ( b 1 a V
0.5
) s t l 0.4 o v0.3 ( b a 0.2 V
0 0
0 0.002
0.004
0.006
0.008
0.01
I (A)
Figure 4. Vab vs. I (Second trial for Daniell cell)
Current I was calculated from the measured voltages and
resistances by Ohm’s Law, I = . With the complete data, the
internal resistances r were calculated through the equation r
0.2
I (A)
0.3
With the complete data, the internal resistances r were 0
=
0.1
Figure 5. Vab vs. I (First trial for carbon zinc)
0.1
Calculated r (Ω) 4.00 4.00 4.00 4.00 4.00 Average r = 4.00 Ω
which was derived earlier. It should be noted from the
calculated through the equation r =
which was derived
earlier. It should be noted from the data that as the external resistance increases, the current decreases. The internal resistance increases together with the external resistance and the average internal resistance obtained is 4.00 Ω, which is generally lower than that of a Daniell cell’s. In the graph, the slope determines the internal resistance r. It was computed through m =
. In this trial, m=
; m = -4. The
negative sign in the slope indicates an inverse relationship between the terminal voltage and the current. The internal resistance from slope is equal to 4 Ω, a value which is
equivalent to the average r, which is 4 Ω. The value of emf Ɛ can also be obtained from the graph through the equation y = mx + b. Y-intercept b is equal to the emf Ɛ. Getting emf Ɛ, 1.65 = (-4)(0.25) + b. The equation yielded b = 2.65, a value equivalent to the measured emf 2.65 V. V. CONCLUSION The results obtained in the two parts of the experiment yielded very small discrepancies between the values measured and calculated. This proves that the equations verify the theories and laws formulated by renowned physicists. From the beginning of the experiment, it was expected that the Daniell cell would have a higher internal resistance than the carbon zinc battery, and it was confirmed in the experiment. Therefore, a dry cell is seen as a better battery than a Daniell cell. It was also verified that as the current increases, the terminal voltage decreases across both cells. Through the experiment, it is concluded that the terminal voltage Vab is less than its emf whenever current is flowing through the battery, because an internal resistance is present in the battery. ACKNOWLEDGMENT The author wishes to thank Ms. Katrina Vargas, first and foremost, for imparting with the author the necessary knowledge in simple circuits and thermodynamics. She also wishes to acknowledge her group mates for the term, Nel Aguilar and Darlene Campado. Lastly, she also gives her thanks for the assistance and support of the DLSU Physics department.
R EFERENCES [1] H. D. Young, et al., “Current, Resistance, and Electromotive Force,” in Sears and Zemansky’s University Physics with Modern Physics, 13 th ed. San Francisco, CA: J. Smith, 2004, pp. 814-831. [2] J. D. Cutnell and K. W. Johnson, “Circuits,” in Physics, 7th ed. Danvers, MA: Wiley, 2007, p. 603. [3] De La Salle University Physics Department, Experiment 7: EMF, Terminal Voltage, and Internal Resistance. Manila, Philippines: De La Salle University, 2013. [4] R. Serway and J. Jewett, “Direct-Current Circuits,” in Physics for Scientists and Engineers with Modern Physics , 9th ed. Boston, MA: M. Finch and C. Hartford, 2008, pp. 833-834.