Internal Resistance of Battery
The main goal of this project study is to find internal resistance of a battery with respect to time. Information received from measurement and calculation of internal resistance would allow finding the battery that sustains their energy for longest period of time
Content
EXPERIMENTAL DETERMINATION OF
PHYSICS
INTERNAL RESISTANCE OF BATTERY
AATISH RENGAN
Class XII
ABHINAV PUBLIC SCHOOL
PITAMPURA NEW DELHI
1
PHYSICS Experimental Determination Of
INTERNAL RESISTANCE OF BATTERY
SUBMISSION
This Project is submitted before Ms. Anu Sagar Madam, my Physics Teacher
It is my foremost duty
to express my deep
regards, respects & gratitude to my teacher, for not only the guidance & supervision but also for the inspiration, motivation, and sense of direction that are instilled in my persona towards biology in special and inquisitiveness towards in general. I submit this study report before Ms. Anu Sagar Madam, the guiding light of this study. The numerous helps, assistance and comforts from lab personnel who gave me and made available various specimens, materials chemicals and equipments for the investigation are of great importance and I acknowledge them with humility.
2
Aatish Rengan
3
CONTENTS
d.e.s.r.i.p.t.i.o.n
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
MEASUREMENT OF INTERNAL RESISTANCE OF AA BATTERIES Abstract Theoretical Considerations Kirchoff”s Voltage Law Ohm’s Law Experimental Procedure Results Discussion Conclusion ADVANCED READINGS The Development of battery Battery types Primary batteries Secondary batteries Lead-Acid batteries AA batteries AAA batteries Nickel-Cadmium batteries Lithium-Ion batteries Nickel-Metal Hydride batteries Wattage, Volts, Ampere, etc.. Appendix Bibliography
p.a. g.e
4
5 5 6 8 11 12 15 16 17 17 18 19 19 20 22 23 24 24 25 26 28 30
4
MEASUREMENT OF INTERNAL RESISTANCE OF AA BATTERIES
The main goal of this project study is to find internal resistance of a battery with respect to time. Information received from measurement and calculation of internal resistance would allow finding the battery that sustains their energy for longest period of time
Aatish Rengan
5
Abstract
Battery is designed as a voltage source in series with resistor. For this experiment two AA batteries were used: one of them had Alkaline chemical composition and the other one carried Zinc-Carbon composition. For calculation of internal resistance, Kirchhoff's Voltage law and Ohm's law were used. The measurements of external resistor voltage were measured every minute until a battery drained down to approximately 0.1 V. Two graphs in the project show a change of external voltage over time and internal resistance over time.
Theoretical Considerations
Figure 1: Typical battery diagram Any battery can be defined as a device that converts "chemical energy directly to electrical energy". [1] This is known as
6
electrochemical reaction. An electrochemical reaction is a "reaction involving the transfer of electrons, and it is that reaction which creates electricity". All types of battery have three main components: the anode, the cathode and electrolyte. The electrolyte conducts the electric current between the anode and the cathode. At the anode, electrons are being sent to the driving circuit. At the cathode, electrons are being accepted. The flow of electrons always occurs from anode to cathode. All batteries have an internal resistance. Any electrical power source can be modeled as a voltage source in series with impedance. This resistance is referred to as "internal resistance". One of the primary requirements for a battery is to have a low internal resistance. The internal resistance of a battery determines its runtime and usually measured in milliohms. The lower the internal resistance of a battery is, the less power is lost. Also, a high internal resistance means that the battery will provide less power. For calculation of internal resistance Kirchhoff's Voltage Law and Ohm's law were used. Measurements of external resistor voltage were measured every minute until a battery drained down to approximately 0.1 /V/. Two graphs in the project shows a change of external voltage over time and internal resistance over time.
Kirchhoff’s Voltage Law (KVL)
Kirchhoff’s voltage law (KVL) states that the algebraic sum of the voltage rises and voltage drops around a loop must be zero.
7
A loop in the above definition means a closed path in the circuit; that is, a path that leaves a node in one direction and returns to that same node from another direction. When deriving the algebraic sum of the voltages, we must assign a plus sign to those voltages where the reference direction agrees with the direction of the loop, and negative signs in the opposite case. The following short example shows the use of Kirchhoff’s voltage law. Find the voltage across resistor R2, given that the source voltage, VS = 100 V and that the voltage across resistor R1 is V1 = 40 V. The solution using Kirchhoff’s voltage law: -VS + V1 + V2 =0, or VS = V1 + V2 hence: V2 = VS – V1 = 100-40 = 60V
8
Another way to state Kirchhoff’s voltage law is: the applied voltage of a series circuit equals the sum of the voltage drops across the series elements. Note that normally we don’t know the voltages of the resistors (unless we measure them), and we need to use both Kirchhoff’s laws for the solution.
Ohm’s Law
Ohm's law states that the current through a conductor between two points is directly proportional to the potential difference across the two points. Introducing the constant of proportionality, the resistance,[1] one arrives at the usual mathematical equation that describes this relationship:
where I is the current through the conductor in units of amperes, V is the potential difference measured across the conductor in units of volts, and R is the resistance of the conductor in units of ohms.
9
More specifically, Ohm's law states that the R in this relation is constant, independent of the current. Ideal batteries differ from real batteries; a real battery has an internal resistance – due to the nature of the battery. The nature of the real battery is determined by its internal chemical reaction.
Nature of Battery and Internal Resistance The darkened ends of the battery represent the products of the chemical reaction used to produce an emf. The green portion shows the unused reactants, which must now pass through the dark regions to produce an emf. The products contribute to the internal resistance of the battery.
The battery produces an emf. The internal resistance of the battery is r. Since the established circuit is a series one, Ir = IR = IT. Now, if an ideal voltmeter was placed in parallel across the rheostat, the measured voltage should theoretically be equal to the potential difference across the real battery, measured by another ideal voltmeter. Since in a series circuit Vr + VR = VT, it can be said that: VT = emf = Vr + VR = Vr + VBATT The equation describing internal resistance can be derived using the above Equation emf - Vr = VBATT, and Vr = Ir by definition
10
so emf - Ir = VBATT
Figure 2 shows a typical battery in series with load resistor.
Figure 2: Diagram of a battery in parallel with Resistor
• •
• r is the unknown internal resistance • Rload is external parallel resistor, i.e., ~0.08 /Ω/. • is e.m.f. E.M.F = voltage across internal resistance+ voltage across load (open circuit voltage (V0)) • i is the current flowing into the circuit
Using basic Kirchhoff's Voltage Law, the equation of the circuit becomes:
In the project R=10 Ω. The goal is to derive the formula to find r. Thus, Equation (1) can be rewritten as:
11
Initial voltage (V0) will be calculated in the beginning of the experiment for each battery.
V will be measured every minute.
Using this information, it will be possible to determine internal resistance (r).
Experimental Procedure
In this experiment I have used two kinds of AA batteries with different chemical composition: alkaline or carbon Zinc. Dura Cell Heavy Duty Alkaline Carbon - Zinc
Table 1: Chemical Composition in batteries
In addition to the batteries, a multimeter, breadboard, controlled resistance box, and a breadboard kit were used in this experiment.
Figure 3: Diagram of Circuit that was used to find voltage over time
In the beginning of the experiment, the open circuit voltage (V0)
was measured with the multimeter at the battery terminals. The
resistance that was used was 0.08/Ω/. The next step was to connect the resistance box to the breadboard
12
so that the voltmeter would be able to measure the parallel resistance.
This data would be used in the Equation Since this formula uses open circuit voltage, and the voltage across the external resistor, , the measurement were taken every 1 minute to have more precise data. The information was typed into an Excel Spreadsheet, and using the above equation for internal resistance (r) the internal resistance would be determined.
Results
The results in the beginning of the experiment were the initial voltage of the battery for each chemical composition.
Table 2: Initial Voltage of "Duracell" and "Heavy duty" batteries
Duracell Heavy duty
1.5861 1.6521
The Figure 4 shows the change the voltage across the external resistor with respect to time. The final voltage measurement was approximately 0.1 V.
Using the Equation for Internal Resistance (r), it was possible to find internal resistance of the battery as it changes with respect to time as plotted in Figure (4). The values of internal resistance are given in Excel Spreadsheet as the Appendix.
13
Figure 4: Graph of external voltage change with respect to time.
14
Figure 5: Graph of Internal Resistance plotted over time
15
Discussion
After careful analysis of the diagrams, it becomes possible to conclude that external voltage and internal resistance have the same properties. External voltage decreases over the time and internal resistance increases over the same amount of time. The external voltage constantly decreases and this is showed in Figure 4. At the same time, internal resistance constantly increases over the same amount of time. This is shown in Figure 4. Using Ohm's law it would be possible to get the same result, since Ohm's law shows inverse relationship between current and time. According to Figure (4) and Figure (5), it is possible to conclude that the battery that has faster increase in internal resistance will be worse at sustaining energy and power. For both batteries measurements were taken until voltage become 0.1 V, so it is possible to conclude that the battery that held the charge for the longest time is the higher-quality battery. Even though, the electrical component of the battery was very important, the chemical process in a battery actually produced the power; with voltage decreasing an internal resistance would increase and this would produce a "high mW reading that will trigger an early 'low battery' indication on a seemingly good battery" [3]. Duracell battery maintained its charge of 0.08412 V at 50 minutes of time elapsed.
16
Conclusion
The goal of this experiment was to determine the internal resistance of a battery, and compare its performance against that of others. Since, in this experiment two different batteries, with two different chemical compositions were used, it was easy to see a decrease in external voltage and an increase in internal resistance with respect to time. After the equivalent circuit was created, the basic Kirchhoff's Voltage Law and Ohm's Law were applied to find internal resistance. With the data, it becomes possible to find the battery that can maintain the energy for the longest time.
Duracell sustained a charge of 0.08412 Volt for 50 Minutes
17
ADVANCED READING The Development of Battery
Batteries are a portable source of electricity. Modern batteries have become amazing powerhouses for today’s portable devices. They have a fascinating history, with men and women across the world striving to harness the remarkable properties of electricity and make them available everywhere. All kinds of batteries are crucial in modern life. In 1800, after extensive experimentation, repeatedly of Galvani's experiments many times with many different materials, Alessandro Volta, a university professor in Padova, developed the voltaic pile. The original voltaic pile consisted of a pile of zinc and silver discs and between alternating discs, a piece of cardboard that had been soaked in saltwater. A wire connecting the bottom zinc disc to the top silver disc could produce repeated sparks. Batteries are used in many ways. Some are disposable, others are rechargeable. Batteries become a primary source of power for a lot of electrical devices. They can be used in many
18
different electrical devices, for example: boats, cars, watches, radios, phones and Mp3 players, etc.
A battery has a positive and a negative electrode. The positive electrode is called a cathode, and the negative electrode is called an anode. In batteries, each electrode contains a different metal. In an alkaline battery, the anode metal is manganese dioxide and the metal in the cathode is zinc. To separate the anode from the cathode there is an electrolyte. The negative electrons want to get to the cathode but the electrolyte blocks the way. To power a light, for example, the electrons go though a circuit, powers the light and arrives at the positive end (cathode) of the battery.
Battery Types
Batteries are divided into two broad categories: primary and secondary batteries. Different chemicals can be combined to make batteries. Some combinations are low cost but also low power, others can store huge power at huge prices. Lead-acid batteries offer the best
19
balance of capacity per dollar and it’s a common battery used in stand-alone power systems.
Primary batteries
Primary batteries can produce current immediately on assembly. Disposable batteries are to be used once and discarded. Disposable primary cells cannot be reliably recharged, since the chemical reactions are not easily reversible and active materials may not return to their original forms. Common types of disposable batteries include zinc–carbon batteries and alkaline batteries. In general, these have higher energy densities than rechargeable batteries,[36] but disposable batteries do not fare well under high-drain applications with loads under 75 ohms.
Secondary batteries
Secondary batteries must be charged before use; they are usually assembled with active materials in the discharged state. Rechargeable batteries or secondary cells can be recharged by applying electric current, which reverses the chemical reactions that occur during its use.
20
The oldest form of rechargeable battery is the lead–acid battery. Its low manufacturing cost and its high surge current levels make its use common where a large capacity (over approximately 10 Ah) is required or where the weight and ease of handling are not concerns.
Lead-Acid Batteries
The lead-acid battery cell consists of positive and negative lead plates of different composition suspended in a sulfuric acid solution called electrolyte. When cells discharge, sulphur molecules from the electrolyte bond with the lead plates and release electrons. When the cell recharges, excess electrons go
21
back to the electrolyte. A battery develops voltage from this chemical reaction. Electricity is the flow of electrons. In a typical lead-acid battery, the voltage is approximately 2 volts per cell regardless of cell size. Electricity flows from the battery as soon as there is a circuit between the positive and negative terminals. This happens when any load (appliance) that needs electricity is connected to the battery. Good care and caution should be used at all times when handling a battery. Improper battery use can result in explosion. Read all documentation included with your battery in its entirety. A common lead–acid battery, the modern car battery, can, deliver a peak current of 450 amperes. An improved type of liquid electrolyte battery is the sealed valve regulated lead–acid battery (VRLA battery), Other portable rechargeable batteries include several "dry cell" types, which are sealed units and are, therefore, useful in appliances such as mobile phones and laptop computers. Cells of this type (in order of increasing power density and cost) include nickel–cadmium (NiCd), nickel–zinc (NiZn), nickel metal hydride (NiMH), and lithium-ion (Li-ion) cells. By far, Li-ion has the highest share of the dry cell rechargeable market. Meanwhile, NiMH has replaced NiCd in most applications due to its higher capacity, but NiCd remains in use in power tools,
22
two-way radios, and medical equipment. NiZn is a new technology that is not yet well established commercially.
AA Batteries
The AA battery (sometimes called "double-A"), is the most common battery size. The AA standard actually refers to the physical dimension of the battery: cylindrical, measuring 1.988" (50mm) in height with a diameter of 0.571" (14.5mm). The AA battery is also called an R6. Based on this physical standard, a large number of different AA batteries have actually been developed. They differ in performance, electrical specification, and suitability for various applications.
Zinc-Carbon AA batteries have been available for the longest amount of time. Alkaline AA batteries are the best general purpose AA battery available today. They provide more power then Zinc-Carbon AA batteries, and also work much better at lower temperatures. The cheapest alkaline AA battery comes close to a Zinc-Carbon battery in price, but still exceeds it in performance. The Duracell Ultra M3 is a top-of-the-range alkaline AA battery,
23
that outlasts not just Zinc-Carbon AA batteries, but also several other alkaline AA batteries. More recently lithium AA batteries have emerged to power high drain devices, such as digital cameras. They clearly outperform any alkaline AA battery.
The most economical and environmentally friendly version of the AA battery is the NiMH rechargeable AA battery. Recharging a set of NiMH AA rechargeables use less dangerous materials than the previous generation of NiCd rechargeable batteries. Rechargeable AA batteries are also typically rated at a voltage of 1.2V, rather than the 1.5V nominal voltage of the precharged batteries.
AAA Batteries
The AAA battery (also called R03 or "triple-A"), is the smaller version of the AA battery. All AAA batteries have a height of 1.752" (44.5mm) and a diameter of 0.413" (10.5mm). Most AAA batteries use alkaline technology, with a voltage of 1.5V. The AAA battery is however also available as a rechargeable battery. The NiMH AAA rechargeable battery is rated at 1.2V.
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Both types of batteries may carry any of several main chemical compositions such as: Zinc-Carbon, Alkaline, Lead acid, Lithium ion.
Nickel-Cadmium Batteries
• Enabled the early use of portable power tools, camcorders, laptop • Was computers standard for and portable cellular computers until phones. 1992.
• NiCad batteries have been virtually displaced by NiMH and Li-ion. • Low energy density by weight makes it less desirable for portable computers. • NiCad batteries have a memory that prevents efficient topping up. • NiCads pollute the environment.
• Low cost and high power capability make it the best technology for motor driven portable devices such as power tools. • Uses nickel hydroxide and cadmium electrodes with potassium hydroxide as the electrolyte.
Lithium-ion Batteries
(Li-ion)
25
• •
Very Now
good taking
power market
to share
weight away from
ratio NiMH
• Found in high end laptop computers and cellular phones • Outputs 3v per cell therefore NOT directly interchangeable with normal 1.5v batteries. (sold a unit that replaces 2, 1.5v batteries) • Made from layered sheets of aluminum foil coated with cobalt oxide, which acts as the cathode with the anode made from a thin copper sheet coated with carbon materials. • The thin film cathode and anode are separated by a sheet of plastic, rolled up together in a spiral and immersed in a liquid electrolyte medium of Lithium. • These batteries produce the same energy as NiMH batteries but are 40% smaller, half the weight, and are better for the environment because they don't contain toxic materials such as cadmium or mercury. • Currently more expensive than a comparable NiMH battery. • There are safety issues when charging - Ensure Li-ion batteries are only charged using a battery charger specifically built for the purpose.
Nickel-Metal Batteries
Hydride
Introduced in 1990 Rapidly took market share away from Ni-Cd batteries in the portable computing industry. They differ from
26
Ni-Cd only by their negative electrode which is made of a metal alloy capable of storing a large amount of electrons. Metal hydride is produced as the charging product. The ergy density is almost 50% greater than Ni-Cd.
Wattage, etc.
Volts,
Amps,
One watt delivered for one hour equals one watt-hour. Wattage is the product of current (amps) multiplied by voltage. watt = amps x volt One amp delivered at 120 volts is the same amount of wattage as 10 amps delivered at 12 volts: 1 amp at 120 volts = 10 amps at 12 volts To figure out how much battery capacity it will require to run an appliance for a given time, multiply the appliance wattage times the number of hours it will run to yield the total watthours. Then divide by the battery voltage to get the amp hours.
27
For example, running a 60-watt light bulb for one hour uses 60 watt-hours. If a 12-volt battery is running the light, it will consume 5 amp-hours (60 watt-hours divided by 12 volts equals 5 amp-hours). [1]All batteries have an internal resistance. Any electrical power source can be modeled as a voltage source in series with impedance. This resistance is referred to as "internal resistance". [2] One of the primary requirements for a battery is to have a low internal resistance. The internal resistance of a battery determines its run time and usually measured in milliohms. The lower the internal resistance of a battery is, lesser is the power lost. Also, a high internal resistance means that the battery will provide less power.
28
Appendix
1.Cell Used : Heavy Duty
Zinc) (Carbon-
Battery Voltage (Initial) External Resistance (R) Time Voltage (Min Change s) (V) 1 0.571 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 0.4028 0.3925 0.404 0.3973 0.3948 0.3865 0.379 0.372 0.3618 0.3386 0.3352 0.3189 0.3042 0.2891 0.2762
1.6514 0.08 Ω Internal Resistance (r) 0.151369527 0.247984111 0.256591083 0.247009901 0.252524541 0.254630193 0.2618163 0.268580475 0.275139785 0.285152018 0.310171294 0.314128878 0.334274067 0.354293228 0.376976825 0.398320058
0.26238 0.423513987
2. Cell Used : Duracell Alkaline Battery Voltage 1.5958 (Initial) External Resistance 0.08 Ω (R) Time Voltage Internal (Mins) Change Resistanc (V) e (r) 0.0691401 1 0.856 87 0.0888677 2 0.756 25 3 0.7126 0.0991524 0.1024292 4 0.6998 66 0.1044855 5 0.692 49 0.1072455 6 0.6818 27 0.1091318 7 0.675 52 0.1119759 8 0.665 4 0.1141362 9 0.6576 53 0.1179593 10 0.6449 74 0.1234486 11 0.6275 06 0.1250497 12 0.6226 91 0.1266429 13 0.6178 27 0.1283289 14 0.6128 82 0.1300427 15 0.6078 77 16 0.1324900 0.6008 13 17 0.1346334 0.5948 9
29
18 19 20 21 22 23 24 25 28 30 35
0.24981 0.448849926 0.23615 0.479441033 0.2258 0.505084145 0.2138 0.537923293 0.2052 0.563820663 0.19382 0.601622124 0.17985 0.654567695 0.1721 0.1486 0.1318 0.0972 0.687646717 0.809044415 0.922367223 1.279176955
18 0.5868 19 0.5804 20 0.5725 21 0.565 22 0.5568 23 0.5469 24 0.5357 25 28 30 35 0.5235 0.4829 0.4441 0.1924
0.1375596 46 0.1399586 49 0.1429938 86 0.1459539 82 0.1492816 09 0.1534320 72 0.1583124 88 0.1638662 85 0.1843694 35 0.2074667 87 0.1843694 35 0.1909337 86
30
Bibliography
[1] Battery (electricity)." Wikipedia, the Free Encyclopedia. 3
August 2011. Web. 2 July 2011. " http://en.wikipedia.org/wiki/Battery_(electricity)
[2] Internal resistance. " Wikipedia, the Free Encyclopedia. 3
August 2011. Web. 2 August 2011. " http://en.wikipedia.org/wiki/Internal_resistance [3] I. Buchmann, April, 2001.
http://www.buchmann.ca/Article11-Page1.asp [Accessed August 3, 2011]
Figure 1:
http://www.plumhollow.ca/go-wind/faq-alternative-
energy
Figure 2 and 3:
http://www.physics.udel.edu/~watson/phys345/class/04- batterytesters.html
31
PHYSICS
INTERNAL RESISTANCE OF BATTERY
AATISH RENGAN
Class XII
ABHINAV PUBLIC SCHOOL
PITAMPURA NEW DELHI
1
PHYSICS Experimental Determination Of
INTERNAL RESISTANCE OF BATTERY
SUBMISSION
This Project is submitted before Ms. Anu Sagar Madam, my Physics Teacher
It is my foremost duty
to express my deep
regards, respects & gratitude to my teacher, for not only the guidance & supervision but also for the inspiration, motivation, and sense of direction that are instilled in my persona towards biology in special and inquisitiveness towards in general. I submit this study report before Ms. Anu Sagar Madam, the guiding light of this study. The numerous helps, assistance and comforts from lab personnel who gave me and made available various specimens, materials chemicals and equipments for the investigation are of great importance and I acknowledge them with humility.
2
Aatish Rengan
3
CONTENTS
d.e.s.r.i.p.t.i.o.n
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
MEASUREMENT OF INTERNAL RESISTANCE OF AA BATTERIES Abstract Theoretical Considerations Kirchoff”s Voltage Law Ohm’s Law Experimental Procedure Results Discussion Conclusion ADVANCED READINGS The Development of battery Battery types Primary batteries Secondary batteries Lead-Acid batteries AA batteries AAA batteries Nickel-Cadmium batteries Lithium-Ion batteries Nickel-Metal Hydride batteries Wattage, Volts, Ampere, etc.. Appendix Bibliography
p.a. g.e
4
5 5 6 8 11 12 15 16 17 17 18 19 19 20 22 23 24 24 25 26 28 30
4
MEASUREMENT OF INTERNAL RESISTANCE OF AA BATTERIES
The main goal of this project study is to find internal resistance of a battery with respect to time. Information received from measurement and calculation of internal resistance would allow finding the battery that sustains their energy for longest period of time
Aatish Rengan
5
Abstract
Battery is designed as a voltage source in series with resistor. For this experiment two AA batteries were used: one of them had Alkaline chemical composition and the other one carried Zinc-Carbon composition. For calculation of internal resistance, Kirchhoff's Voltage law and Ohm's law were used. The measurements of external resistor voltage were measured every minute until a battery drained down to approximately 0.1 V. Two graphs in the project show a change of external voltage over time and internal resistance over time.
Theoretical Considerations
Figure 1: Typical battery diagram Any battery can be defined as a device that converts "chemical energy directly to electrical energy". [1] This is known as
6
electrochemical reaction. An electrochemical reaction is a "reaction involving the transfer of electrons, and it is that reaction which creates electricity". All types of battery have three main components: the anode, the cathode and electrolyte. The electrolyte conducts the electric current between the anode and the cathode. At the anode, electrons are being sent to the driving circuit. At the cathode, electrons are being accepted. The flow of electrons always occurs from anode to cathode. All batteries have an internal resistance. Any electrical power source can be modeled as a voltage source in series with impedance. This resistance is referred to as "internal resistance". One of the primary requirements for a battery is to have a low internal resistance. The internal resistance of a battery determines its runtime and usually measured in milliohms. The lower the internal resistance of a battery is, the less power is lost. Also, a high internal resistance means that the battery will provide less power. For calculation of internal resistance Kirchhoff's Voltage Law and Ohm's law were used. Measurements of external resistor voltage were measured every minute until a battery drained down to approximately 0.1 /V/. Two graphs in the project shows a change of external voltage over time and internal resistance over time.
Kirchhoff’s Voltage Law (KVL)
Kirchhoff’s voltage law (KVL) states that the algebraic sum of the voltage rises and voltage drops around a loop must be zero.
7
A loop in the above definition means a closed path in the circuit; that is, a path that leaves a node in one direction and returns to that same node from another direction. When deriving the algebraic sum of the voltages, we must assign a plus sign to those voltages where the reference direction agrees with the direction of the loop, and negative signs in the opposite case. The following short example shows the use of Kirchhoff’s voltage law. Find the voltage across resistor R2, given that the source voltage, VS = 100 V and that the voltage across resistor R1 is V1 = 40 V. The solution using Kirchhoff’s voltage law: -VS + V1 + V2 =0, or VS = V1 + V2 hence: V2 = VS – V1 = 100-40 = 60V
8
Another way to state Kirchhoff’s voltage law is: the applied voltage of a series circuit equals the sum of the voltage drops across the series elements. Note that normally we don’t know the voltages of the resistors (unless we measure them), and we need to use both Kirchhoff’s laws for the solution.
Ohm’s Law
Ohm's law states that the current through a conductor between two points is directly proportional to the potential difference across the two points. Introducing the constant of proportionality, the resistance,[1] one arrives at the usual mathematical equation that describes this relationship:
where I is the current through the conductor in units of amperes, V is the potential difference measured across the conductor in units of volts, and R is the resistance of the conductor in units of ohms.
9
More specifically, Ohm's law states that the R in this relation is constant, independent of the current. Ideal batteries differ from real batteries; a real battery has an internal resistance – due to the nature of the battery. The nature of the real battery is determined by its internal chemical reaction.
Nature of Battery and Internal Resistance The darkened ends of the battery represent the products of the chemical reaction used to produce an emf. The green portion shows the unused reactants, which must now pass through the dark regions to produce an emf. The products contribute to the internal resistance of the battery.
The battery produces an emf. The internal resistance of the battery is r. Since the established circuit is a series one, Ir = IR = IT. Now, if an ideal voltmeter was placed in parallel across the rheostat, the measured voltage should theoretically be equal to the potential difference across the real battery, measured by another ideal voltmeter. Since in a series circuit Vr + VR = VT, it can be said that: VT = emf = Vr + VR = Vr + VBATT The equation describing internal resistance can be derived using the above Equation emf - Vr = VBATT, and Vr = Ir by definition
10
so emf - Ir = VBATT
Figure 2 shows a typical battery in series with load resistor.
Figure 2: Diagram of a battery in parallel with Resistor
• •
• r is the unknown internal resistance • Rload is external parallel resistor, i.e., ~0.08 /Ω/. • is e.m.f. E.M.F = voltage across internal resistance+ voltage across load (open circuit voltage (V0)) • i is the current flowing into the circuit
Using basic Kirchhoff's Voltage Law, the equation of the circuit becomes:
In the project R=10 Ω. The goal is to derive the formula to find r. Thus, Equation (1) can be rewritten as:
11
Initial voltage (V0) will be calculated in the beginning of the experiment for each battery.
V will be measured every minute.
Using this information, it will be possible to determine internal resistance (r).
Experimental Procedure
In this experiment I have used two kinds of AA batteries with different chemical composition: alkaline or carbon Zinc. Dura Cell Heavy Duty Alkaline Carbon - Zinc
Table 1: Chemical Composition in batteries
In addition to the batteries, a multimeter, breadboard, controlled resistance box, and a breadboard kit were used in this experiment.
Figure 3: Diagram of Circuit that was used to find voltage over time
In the beginning of the experiment, the open circuit voltage (V0)
was measured with the multimeter at the battery terminals. The
resistance that was used was 0.08/Ω/. The next step was to connect the resistance box to the breadboard
12
so that the voltmeter would be able to measure the parallel resistance.
This data would be used in the Equation Since this formula uses open circuit voltage, and the voltage across the external resistor, , the measurement were taken every 1 minute to have more precise data. The information was typed into an Excel Spreadsheet, and using the above equation for internal resistance (r) the internal resistance would be determined.
Results
The results in the beginning of the experiment were the initial voltage of the battery for each chemical composition.
Table 2: Initial Voltage of "Duracell" and "Heavy duty" batteries
Duracell Heavy duty
1.5861 1.6521
The Figure 4 shows the change the voltage across the external resistor with respect to time. The final voltage measurement was approximately 0.1 V.
Using the Equation for Internal Resistance (r), it was possible to find internal resistance of the battery as it changes with respect to time as plotted in Figure (4). The values of internal resistance are given in Excel Spreadsheet as the Appendix.
13
Figure 4: Graph of external voltage change with respect to time.
14
Figure 5: Graph of Internal Resistance plotted over time
15
Discussion
After careful analysis of the diagrams, it becomes possible to conclude that external voltage and internal resistance have the same properties. External voltage decreases over the time and internal resistance increases over the same amount of time. The external voltage constantly decreases and this is showed in Figure 4. At the same time, internal resistance constantly increases over the same amount of time. This is shown in Figure 4. Using Ohm's law it would be possible to get the same result, since Ohm's law shows inverse relationship between current and time. According to Figure (4) and Figure (5), it is possible to conclude that the battery that has faster increase in internal resistance will be worse at sustaining energy and power. For both batteries measurements were taken until voltage become 0.1 V, so it is possible to conclude that the battery that held the charge for the longest time is the higher-quality battery. Even though, the electrical component of the battery was very important, the chemical process in a battery actually produced the power; with voltage decreasing an internal resistance would increase and this would produce a "high mW reading that will trigger an early 'low battery' indication on a seemingly good battery" [3]. Duracell battery maintained its charge of 0.08412 V at 50 minutes of time elapsed.
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Conclusion
The goal of this experiment was to determine the internal resistance of a battery, and compare its performance against that of others. Since, in this experiment two different batteries, with two different chemical compositions were used, it was easy to see a decrease in external voltage and an increase in internal resistance with respect to time. After the equivalent circuit was created, the basic Kirchhoff's Voltage Law and Ohm's Law were applied to find internal resistance. With the data, it becomes possible to find the battery that can maintain the energy for the longest time.
Duracell sustained a charge of 0.08412 Volt for 50 Minutes
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ADVANCED READING The Development of Battery
Batteries are a portable source of electricity. Modern batteries have become amazing powerhouses for today’s portable devices. They have a fascinating history, with men and women across the world striving to harness the remarkable properties of electricity and make them available everywhere. All kinds of batteries are crucial in modern life. In 1800, after extensive experimentation, repeatedly of Galvani's experiments many times with many different materials, Alessandro Volta, a university professor in Padova, developed the voltaic pile. The original voltaic pile consisted of a pile of zinc and silver discs and between alternating discs, a piece of cardboard that had been soaked in saltwater. A wire connecting the bottom zinc disc to the top silver disc could produce repeated sparks. Batteries are used in many ways. Some are disposable, others are rechargeable. Batteries become a primary source of power for a lot of electrical devices. They can be used in many
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different electrical devices, for example: boats, cars, watches, radios, phones and Mp3 players, etc.
A battery has a positive and a negative electrode. The positive electrode is called a cathode, and the negative electrode is called an anode. In batteries, each electrode contains a different metal. In an alkaline battery, the anode metal is manganese dioxide and the metal in the cathode is zinc. To separate the anode from the cathode there is an electrolyte. The negative electrons want to get to the cathode but the electrolyte blocks the way. To power a light, for example, the electrons go though a circuit, powers the light and arrives at the positive end (cathode) of the battery.
Battery Types
Batteries are divided into two broad categories: primary and secondary batteries. Different chemicals can be combined to make batteries. Some combinations are low cost but also low power, others can store huge power at huge prices. Lead-acid batteries offer the best
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balance of capacity per dollar and it’s a common battery used in stand-alone power systems.
Primary batteries
Primary batteries can produce current immediately on assembly. Disposable batteries are to be used once and discarded. Disposable primary cells cannot be reliably recharged, since the chemical reactions are not easily reversible and active materials may not return to their original forms. Common types of disposable batteries include zinc–carbon batteries and alkaline batteries. In general, these have higher energy densities than rechargeable batteries,[36] but disposable batteries do not fare well under high-drain applications with loads under 75 ohms.
Secondary batteries
Secondary batteries must be charged before use; they are usually assembled with active materials in the discharged state. Rechargeable batteries or secondary cells can be recharged by applying electric current, which reverses the chemical reactions that occur during its use.
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The oldest form of rechargeable battery is the lead–acid battery. Its low manufacturing cost and its high surge current levels make its use common where a large capacity (over approximately 10 Ah) is required or where the weight and ease of handling are not concerns.
Lead-Acid Batteries
The lead-acid battery cell consists of positive and negative lead plates of different composition suspended in a sulfuric acid solution called electrolyte. When cells discharge, sulphur molecules from the electrolyte bond with the lead plates and release electrons. When the cell recharges, excess electrons go
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back to the electrolyte. A battery develops voltage from this chemical reaction. Electricity is the flow of electrons. In a typical lead-acid battery, the voltage is approximately 2 volts per cell regardless of cell size. Electricity flows from the battery as soon as there is a circuit between the positive and negative terminals. This happens when any load (appliance) that needs electricity is connected to the battery. Good care and caution should be used at all times when handling a battery. Improper battery use can result in explosion. Read all documentation included with your battery in its entirety. A common lead–acid battery, the modern car battery, can, deliver a peak current of 450 amperes. An improved type of liquid electrolyte battery is the sealed valve regulated lead–acid battery (VRLA battery), Other portable rechargeable batteries include several "dry cell" types, which are sealed units and are, therefore, useful in appliances such as mobile phones and laptop computers. Cells of this type (in order of increasing power density and cost) include nickel–cadmium (NiCd), nickel–zinc (NiZn), nickel metal hydride (NiMH), and lithium-ion (Li-ion) cells. By far, Li-ion has the highest share of the dry cell rechargeable market. Meanwhile, NiMH has replaced NiCd in most applications due to its higher capacity, but NiCd remains in use in power tools,
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two-way radios, and medical equipment. NiZn is a new technology that is not yet well established commercially.
AA Batteries
The AA battery (sometimes called "double-A"), is the most common battery size. The AA standard actually refers to the physical dimension of the battery: cylindrical, measuring 1.988" (50mm) in height with a diameter of 0.571" (14.5mm). The AA battery is also called an R6. Based on this physical standard, a large number of different AA batteries have actually been developed. They differ in performance, electrical specification, and suitability for various applications.
Zinc-Carbon AA batteries have been available for the longest amount of time. Alkaline AA batteries are the best general purpose AA battery available today. They provide more power then Zinc-Carbon AA batteries, and also work much better at lower temperatures. The cheapest alkaline AA battery comes close to a Zinc-Carbon battery in price, but still exceeds it in performance. The Duracell Ultra M3 is a top-of-the-range alkaline AA battery,
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that outlasts not just Zinc-Carbon AA batteries, but also several other alkaline AA batteries. More recently lithium AA batteries have emerged to power high drain devices, such as digital cameras. They clearly outperform any alkaline AA battery.
The most economical and environmentally friendly version of the AA battery is the NiMH rechargeable AA battery. Recharging a set of NiMH AA rechargeables use less dangerous materials than the previous generation of NiCd rechargeable batteries. Rechargeable AA batteries are also typically rated at a voltage of 1.2V, rather than the 1.5V nominal voltage of the precharged batteries.
AAA Batteries
The AAA battery (also called R03 or "triple-A"), is the smaller version of the AA battery. All AAA batteries have a height of 1.752" (44.5mm) and a diameter of 0.413" (10.5mm). Most AAA batteries use alkaline technology, with a voltage of 1.5V. The AAA battery is however also available as a rechargeable battery. The NiMH AAA rechargeable battery is rated at 1.2V.
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Both types of batteries may carry any of several main chemical compositions such as: Zinc-Carbon, Alkaline, Lead acid, Lithium ion.
Nickel-Cadmium Batteries
• Enabled the early use of portable power tools, camcorders, laptop • Was computers standard for and portable cellular computers until phones. 1992.
• NiCad batteries have been virtually displaced by NiMH and Li-ion. • Low energy density by weight makes it less desirable for portable computers. • NiCad batteries have a memory that prevents efficient topping up. • NiCads pollute the environment.
• Low cost and high power capability make it the best technology for motor driven portable devices such as power tools. • Uses nickel hydroxide and cadmium electrodes with potassium hydroxide as the electrolyte.
Lithium-ion Batteries
(Li-ion)
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• •
Very Now
good taking
power market
to share
weight away from
ratio NiMH
• Found in high end laptop computers and cellular phones • Outputs 3v per cell therefore NOT directly interchangeable with normal 1.5v batteries. (sold a unit that replaces 2, 1.5v batteries) • Made from layered sheets of aluminum foil coated with cobalt oxide, which acts as the cathode with the anode made from a thin copper sheet coated with carbon materials. • The thin film cathode and anode are separated by a sheet of plastic, rolled up together in a spiral and immersed in a liquid electrolyte medium of Lithium. • These batteries produce the same energy as NiMH batteries but are 40% smaller, half the weight, and are better for the environment because they don't contain toxic materials such as cadmium or mercury. • Currently more expensive than a comparable NiMH battery. • There are safety issues when charging - Ensure Li-ion batteries are only charged using a battery charger specifically built for the purpose.
Nickel-Metal Batteries
Hydride
Introduced in 1990 Rapidly took market share away from Ni-Cd batteries in the portable computing industry. They differ from
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Ni-Cd only by their negative electrode which is made of a metal alloy capable of storing a large amount of electrons. Metal hydride is produced as the charging product. The ergy density is almost 50% greater than Ni-Cd.
Wattage, etc.
Volts,
Amps,
One watt delivered for one hour equals one watt-hour. Wattage is the product of current (amps) multiplied by voltage. watt = amps x volt One amp delivered at 120 volts is the same amount of wattage as 10 amps delivered at 12 volts: 1 amp at 120 volts = 10 amps at 12 volts To figure out how much battery capacity it will require to run an appliance for a given time, multiply the appliance wattage times the number of hours it will run to yield the total watthours. Then divide by the battery voltage to get the amp hours.
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For example, running a 60-watt light bulb for one hour uses 60 watt-hours. If a 12-volt battery is running the light, it will consume 5 amp-hours (60 watt-hours divided by 12 volts equals 5 amp-hours). [1]All batteries have an internal resistance. Any electrical power source can be modeled as a voltage source in series with impedance. This resistance is referred to as "internal resistance". [2] One of the primary requirements for a battery is to have a low internal resistance. The internal resistance of a battery determines its run time and usually measured in milliohms. The lower the internal resistance of a battery is, lesser is the power lost. Also, a high internal resistance means that the battery will provide less power.
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Appendix
1.Cell Used : Heavy Duty
Zinc) (Carbon-
Battery Voltage (Initial) External Resistance (R) Time Voltage (Min Change s) (V) 1 0.571 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 0.4028 0.3925 0.404 0.3973 0.3948 0.3865 0.379 0.372 0.3618 0.3386 0.3352 0.3189 0.3042 0.2891 0.2762
1.6514 0.08 Ω Internal Resistance (r) 0.151369527 0.247984111 0.256591083 0.247009901 0.252524541 0.254630193 0.2618163 0.268580475 0.275139785 0.285152018 0.310171294 0.314128878 0.334274067 0.354293228 0.376976825 0.398320058
0.26238 0.423513987
2. Cell Used : Duracell Alkaline Battery Voltage 1.5958 (Initial) External Resistance 0.08 Ω (R) Time Voltage Internal (Mins) Change Resistanc (V) e (r) 0.0691401 1 0.856 87 0.0888677 2 0.756 25 3 0.7126 0.0991524 0.1024292 4 0.6998 66 0.1044855 5 0.692 49 0.1072455 6 0.6818 27 0.1091318 7 0.675 52 0.1119759 8 0.665 4 0.1141362 9 0.6576 53 0.1179593 10 0.6449 74 0.1234486 11 0.6275 06 0.1250497 12 0.6226 91 0.1266429 13 0.6178 27 0.1283289 14 0.6128 82 0.1300427 15 0.6078 77 16 0.1324900 0.6008 13 17 0.1346334 0.5948 9
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18 19 20 21 22 23 24 25 28 30 35
0.24981 0.448849926 0.23615 0.479441033 0.2258 0.505084145 0.2138 0.537923293 0.2052 0.563820663 0.19382 0.601622124 0.17985 0.654567695 0.1721 0.1486 0.1318 0.0972 0.687646717 0.809044415 0.922367223 1.279176955
18 0.5868 19 0.5804 20 0.5725 21 0.565 22 0.5568 23 0.5469 24 0.5357 25 28 30 35 0.5235 0.4829 0.4441 0.1924
0.1375596 46 0.1399586 49 0.1429938 86 0.1459539 82 0.1492816 09 0.1534320 72 0.1583124 88 0.1638662 85 0.1843694 35 0.2074667 87 0.1843694 35 0.1909337 86
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Bibliography
[1] Battery (electricity)." Wikipedia, the Free Encyclopedia. 3
August 2011. Web. 2 July 2011. " http://en.wikipedia.org/wiki/Battery_(electricity)
[2] Internal resistance. " Wikipedia, the Free Encyclopedia. 3
August 2011. Web. 2 August 2011. " http://en.wikipedia.org/wiki/Internal_resistance [3] I. Buchmann, April, 2001.
http://www.buchmann.ca/Article11-Page1.asp [Accessed August 3, 2011]
Figure 1:
http://www.plumhollow.ca/go-wind/faq-alternative-
energy
Figure 2 and 3:
http://www.physics.udel.edu/~watson/phys345/class/04- batterytesters.html
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