7
CHAPTER
Cells and Batteries
IN ELECTRICITY, WE CALL A UNIT SOURCE OF DC ENERGY A CELL. WHEN WE CONNECT TWO OR MORE cells in series, parallel, or series-parallel, we obtain a battery. Numerous types of cells and batteries exist, and inventors keep discovering more.
Electrochemical Energy
Early in the history of electricity science, physicists noticed that when metals came into contact with certain chemical solutions, a potential difference sometimes appeared between the pieces of metal. These experimenters had discovered the first electrochemical cells.
A piece of lead and a piece of lead dioxide immersed in an acid solution (Fig. 7-1) acquire a persistent potential difference. In the original experiments, scientists detected this voltage by connecting a galvanometer between the pieces of metal. A resistor in series with the galvanometer prevents excessive current from flowing, and keeps acid from “boiling out” of the cell. Nowadays, of course, we can use a laboratory voltmeter to measure the potential difference.
7-1 Construction of a lead-acid electrochemical cell.
If we draw current from a cell, such as the one shown in Fig. 7-1, for a long time by connecting a resistor between its terminals, the current will gradually decrease, and the electrodes will become coated. Eventually, all the chemical energy in the acid will have turned into electrical energy and dissipated as thermal energy in the resistor and the cell’s own chemical solution, escaping into the surrounding environment in the form of kinetic energy.
Primary and Secondary Cells and Batteries
Some electrical cells, once their chemical energy has been used up, must be thrown away. We call such a device a primary cell. Other kinds of cells, such as the lead-acid type, can get their chemical energy back again by means of recharging. Such a cell constitutes a secondary cell.
Primary cells include the ones you usually put in a flashlight, in a transistor radio, and in various other consumer devices. They use dry electrolyte (conductive chemical) pastes along with metal electrodes, and go by names, such as dry cell, zinc-carbon cell, or alkaline cell. When you encounter a shelf full of “batteries” in a department store, you’ll see primary cells that go by names, such as AAA batteries, D batteries, camera batteries, and watch batteries. (These are actually cells, not true batteries.) You’ll also see 9-V transistor batteries and large 6-V lantern batteries.
You can also find secondary cells in consumer stores. They cost several times as much as ordinary dry cells, and the requisite charging unit also costs a few dollars. But if you take care of rechargeable cells, you can use them hundreds of times, and they’ll pay for themselves several times over.
The battery in your car or truck consists of several secondary cells connected in series. These cells recharge from the alternator (a form of generator) or from an external charging unit. A typical automotive battery has cells like the one in Fig. 7-1. You should never short-circuit the terminals of such a battery or connect a load to it that draws a large amount of current because the acid (sulfuric acid) can erupt out of the battery container. Serious skin and eye injuries can result. In fact, it’s a bad idea to short-circuit any cell or battery because it can rupture and damage surrounding materials, wiring, and components. Some “shorted-out” cells and batteries can heat up enough to catch on fire.
Cells in Series and Parallel
When we want to make a battery from two or more electrochemical cells, we should always use cells having the same chemical composition and the same physical size and mass. In other words, all the cells in the set should be identical! Assuming we heed that principle, we can generalize as follows.
• When we connect cells in series, the no-load output voltage (when we don’t make the cells deliver any current) multiplies by the number of cells, while the maximum deliverable current (when we make the cells produce as much current as they can) equals the maximum deliverable current from only one cell.
• When we connect cells in parallel, the no-load output voltage of the whole set equals the no-load output voltage of only one cell, while the maximum deliverable current from the set multiplies according to the number of cells.
The Weston Standard Cell
A standard cell produces a precise and predictable no-load output voltage for use in scientific laboratories. The Weston standard cell (or simply the Weston cell) generates 1.018 V DC at room temperature. It employs a solution of cadmium sulfate, a positive electrode made from mercury sulfate, and a negative electrode made from mercury and cadmium. A two-chambered container holds the chemicals and electrodes (Fig. 7-2).
7-2 Construction of a Weston standard cell.
Most electrochemical cells intended for consumer use produce 1.2 V to 1.8 V DC. The exact output voltage from a new electrochemical cell when we test it under no-load conditions (zero current drain) depends on the chemicals used in its manufacture. Physical size or mass has nothing to do with a cell’s no-load output voltage. Variables in the manufacturing process of a particular type of cell can affect its “new-off-the-shelf” output voltage slightly.
Storage Capacity
Engineers commonly work with two units of electrical energy: the watt-hour (Wh) and the kilowatt-hour (kWh), as we’ve learned. Any electrochemical cell or battery has a certain amount of electrical energy that we can “extract” before it “runs out of juice.” We can quantify that energy in terms of watt-hours or kilowatt-hours. Some engineers express the capacity of a cell or battery of known voltage in units called ampere-hours (Ah).
As an example, a battery with a rating of 2 Ah can provide 2 A for 1 h, or 1 A for 2 h, or 100 mA for 20 h. Infinitely many possibilities exist, as long as the product of the current (in amperes) and the usage time (in hours) equals 2. Practical usage limitations are the shelf life at one extreme, and the maximum deliverable current at the other. We define shelf life as the length of time the battery will last if we never use it at all; this time period might be several years. We define the maximum deliverable current as the highest amount of current that the battery can provide at any moment without suffering a significant decrease in the output voltage because of its own internal resistance.
Small cells have storage capacity ratings of a few milliampere-hours (mAh) up to 100 or 200 mAh. Medium-sized cells can supply 500 mAh to 1 Ah. Large automotive batteries can provide upwards of 50 Ah. The energy capacity in watt-hours equals the ampere-hour capacity multiplied by the battery voltage. For a cell or battery having a particular chemical composition, the storage capacity varies directly in proportion to the physical volume of the device. A cell whose volume equals 20 cubic centimeters (cm3), therefore, has twice the total energy storage capacity of a cell having the same chemical makeup, but that has a volume of only 10 cm3.
An ideal cell or ideal battery (a theoretically perfect one) delivers a constant current for a while, and then the current drops fast (Fig. 7-3). Some types of cells and batteries approach this level of perfection, which we represent graphically as a flat discharge curve. Most cells and batteries are imperfect, and some are far from the ideal, delivering current that declines steadily from the start. When the deliverable current under constant load has tailed off to about half of its initial value, we say that the cell or battery has become “weak.” At this time, we should replace it. If we allow such a cell or battery to run down until the current goes to zero, we call it “dead.” The area under the curve in Fig. 7-3 represents the total capacity of the cell or battery in ampere-hours.
7-3 A flat discharge curve, considered ideal.
“Grocery Store” Cells and Batteries
The cells you see in retail stores provide approximately 1.5 V DC, and are available in sizes known as AAA (very small), AA (small), C (medium large), and D (large). You can also find batteries that deliver 6 or 9 V DC.
Zinc-Carbon Cells
Figure 7-4 is a “translucent” drawing of a zinc-carbon cell. The zinc forms the case, which serves as the negative electrode. A carbon rod constitutes the positive electrode. The electrolyte comprises a paste of manganese dioxide and carbon. Zinc-carbon cells don’t cost very much. They work well at moderate temperatures, and in applications where the current drain is moderate to high. They don’t perform well in extreme cold or extreme heat.
7-4 Construction of a zinccarbon electrochemical cell.
Alkaline Cells
The alkaline cell has granular zinc as the negative electrode, potassium hydroxide as the electrolyte, and an element called a polarizer as the positive electrode. The construction resembles that of the zinc-carbon cell. An alkaline cell can work at lower temperatures than a zinc-carbon cell can. The alkaline cell also lasts longer in most electronic devices. It’s the cell of choice for use in transistor radios, calculators, and portable cassette players. The shelf life exceeds that of a zinc-carbon cell. As you might expect, it costs more than a zinc-carbon cell of comparable physical size.
Transistor Batteries
A transistor battery consists of six tiny zinc-carbon or alkaline cells connected in series and enclosed in a small box-shaped case. Each cell supplies 1.5 V, so the battery supplies 9 V. Even though these batteries have more voltage than individual cells, the energy capacity is less than that of a single size C or D cell. The electrical energy that we can get from a cell or battery varies in direct proportion to the amount of chemical energy stored in it—and that, in turn, is a direct function of the volume (physical size) of the cell or the mass (quantity of chemical matter) of the cell. Cells of size C or D have more volume and mass than a transistor battery does, and therefore, contain more stored energy for the same chemical composition. We can find transistor batteries in low-current electronic devices, such as remote-control garage-door openers, television (TV) and hi-fi remote-control units, and electronic calculators.
Lantern Batteries
A so-called lantern battery has much greater mass than a common dry cell or transistor battery, so it lasts much longer and can deliver more current. Lantern batteries are usually rated at 6 V. Two lantern batteries connected in series make a 12-V battery that can power a small Citizens Band (CB) or amateur (“ham”) radio transceiver for a while. Lantern batteries work well in portable locations for medium-power needs.
Miniature Cells and Batteries
In recent years, cells and batteries have become available in many different sizes and shapes besides the old cylindrical cells, transistor batteries, and lantern batteries. Various interesting (and some strange-looking) cells and batteries operate wristwatches, small cameras, and other miniaturized electronic devices.
Silver-Oxide Cells and Batteries
A silver-oxide cell has a button-like shape, and can fit inside a small wristwatch. These types of cells come in various sizes, all with similar appearances. They supply 1.5 V, and offer excellent energy storage capacity considering their low mass. They also have a nearly flat discharge curve, like the one shown in the graph of Fig. 7-3. Zinc-carbon and alkaline cells and batteries, in contrast, have current output that declines more steadily with time, as shown in Fig. 7-5 (a so-called declining discharge curve). We can stack two or more silver-oxide cells to make a battery. Several of these miniature cells, one on top of the other, can provide 6, 9, or 12 V for a transistor radio or other light-duty electronic device.
7-5 A declining discharge curve.
Mercury Cells and Batteries
A mercury cell, also called a mercuric-oxide cell, has properties similar to those of silver-oxide cells. They’re manufactured in the same general form. The main difference, often not of significance, is a somewhat lower voltage per cell: 1.35 V. If we stack up seven of these cells in series to make a battery, the resulting voltage will equal about 9.45 V, close to that of a standard 9-V transistor battery.
Mercury cells and batteries have fallen from favor in recent years because mercury acts as a toxin, even in trace amounts. The mercury concentration accumulates over time in animals and humans. When mercury cells and batteries run down, we must discard them, posing additional problems, because the mercury gradually leaks into the soil, and from there into our food and water supplies.
Lithium Cells and Batteries
Lithium cells gained popularity in the early 1980s. We can find several variations in the chemical makeup of these cells. They all contain lithium, a light, highly reactive metal. Lithium cells typically supply 1.5 V to 3.5 V, depending on the chemistry used in manufacture. These cells, like all other cells, can be stacked to make batteries.
Lithium batteries originally found application as memory backup power supplies for electronic microcomputers. Lithium cells and batteries have superior shelf life. They can last for years in very-low-current applications, such as memory backup or the powering of a digital liquid-crystal-display (LCD) watch or clock. These cells also provide high energy capacity per unit of volume or mass.
Lithium-Polymer (LiPo) Cells and Batteries
LiPo cells produce a voltage of 3.7 V rising to 4.35 V (fully charged) and are, therefore, often used as a single cell or a 7.4-V battery of two cells. Larger batteries are also found in laptops and other high-power devices.
The energy density of a LiPo cell is much higher than any of the other readily available battery technologies. For this reason, they have become the technology of choice for most applications in which a rechargeable battery is needed.
You must use care when charging LiPo cells, as they are prone to catching fire if overcharged. Overdischarging can easily destroy the battery. Some cells include a built-in IC that automatically prevents overcharging or undercharging. In a LiPo battery with two or more cells, each cell should be charged separately, using a special balanced charger.
Lead-Acid Batteries
You’ve seen the basic configuration for a lead-acid cell, which has a solution of sulfuric acid, along with a lead electrode (negative) and a lead-dioxide electrode (positive). These cells are rechargeable.
Automotive batteries comprise series-connected sets of lead-acid cells having a free-flowing liquid acid. You can’t tip such a battery on its side, or turn it upside-down, without running the risk of having some of the acid electrolyte spill out. Some lead-acid batteries have semisolid electrolytes; they find applications in consumer electronic devices, notebook computers, and uninterruptible power supplies (UPSs) that can keep a desktop computer running for a few minutes if the utility power fails.
A large lead-acid battery, such as the one in your car or truck, can store several tens of ampere-hours. The smaller ones, like those in a UPS, have less capacity but more versatility. Their main attributes include the fact you can use and recharge them many times, they don’t cost much money, and you don’t have to worry about the irregular discharge characteristics that some rechargeable cells and batteries have.
Nickel-Based Cells and Batteries
Nickel-based cells include the nickel-cadmium (NICAD or NiCd) type and the nickel-metal-hydride (NiMH) type. Nickel-based batteries are available in packs of cells. You can sometimes plug these packs directly into consumer equipment. In other cases, the batteries actually form part of the device housing. All nickel-based cells are rechargeable. You can put them through hundreds or even thousands of charge/discharge cycles if you take good care of them.
Configurations and Applications
Nickel-based cells come in various sizes and shapes. Cylindrical cells look like ordinary dry cells. You’ll find button cells in cameras, watches, memory backup applications, and other places where miniaturization matters. Flooded cells find application in heavy-duty electronic and electromechanical systems; some of these can store 1000 Ah or more. Spacecraft cells are manufactured in airtight, thermally protected packages that can withstand the rigors of a deep-space environment.
Most orbiting satellites endure total darkness for approximately half the time, and bask in direct sunlight the other half of the time. (The rare exception is the satellite with a carefully prescribed orbit that keeps it above the gray line, or the zone of surface sunrise or sunset. Such a satellite “sees” the sun all the time.) Solar panels can operate while the satellite receives sunlight, but during the times that the earth eclipses the sun, electrochemical batteries must power the electronic equipment on the satellite. The solar panels can charge the electrochemical battery, in addition to powering the satellite, for the “daylight” half of each orbit.
Precautions
Never discharge nickel-based cells all the way until they “totally die.” If you make that mistake, you can cause the polarity of a cell, or of one or more cells in a battery, to permanently reverse, ruining the device for good.
Nickel-based cells and batteries, particularly the NICAD type, sometimes exhibit a bothersome characteristic called memory or memory drain. If you use such a device repeatedly, and you allow it to discharge to the same extent with every cycle, it seems to lose most of its capacity and “die too soon.” You can sometimes “cure” a nickel-based cell or battery of this problem by letting it run down until it stops working properly, recharging it, running it down again, and repeating the cycle numerous times. In stubborn cases, you’ll want to buy a new cell or battery instead of spending a lot of time trying to rejuvenate the old one.
Nickel-based cells and batteries work best if used with charging units that take several hours to fully replenish the charge. So-called high-rate or quick chargers are available, but some of these can force too much current through a cell or battery. It’s best if the charger is made especially for the cell or battery type you use.
In recent years, concern has mounted about the toxic environmental effects of discarded heavy metals, including the cadmium in NICAD cells and batteries. For this reason, NiMH cells and batteries have largely supplanted NICAD types for consumer use. In most practical scenarios, you can directly replace a NICAD device with a NiMH device having the same output voltage and current-delivering capacity.
Photovoltaic Cells and Batteries
The photovoltaic (PV) cell, also called a solar cell, differs fundamentally from the electrochemical cell. A PV cell converts visible light, infrared (IR) rays, and/or ultraviolet (UV) rays directly into DC electricity.
Construction and Performance
Figure 7-6 shows the basic internal construction of a photovoltaic cell. A flat semiconductor P-N junction forms the active region within the device. It has a transparent housing so that radiant energy can directly strike the P-type silicon. The metal ribs, forming the positive electrode, are interconnected by means of tiny wires. The negative electrode consists of a metal backing, called the substrate, placed in contact with the N-type silicon.
7-6 Construction of a silicon photovoltaic (PV) cell.
Most silicon-based solar cells provide about 0.6 V DC in direct sunlight. If the current demand is low, muted sunlight or artificial lamps can produce the full output voltage from a solar cell. As the current demand increases, the cell must receive more intense illumination to produce its full output voltage. A maximum limit exists to the current that a solar cell can deliver, no matter how bright the light. To obtain more current than that, we must connect multiple cells in parallel.
When we connect numerous photovoltaic cells in series-parallel, we obtain a solar panel. A large solar panel might consist of, say, 50 parallel sets of 20 series-connected cells. The series connection boosts the voltage, and the parallel connection increases the current-delivering ability. Sometimes, you’ll find multiple solar panels connected in series or parallel to make vast arrays.
Practical Applications
Solar cells have become cheaper and more efficient in recent years, as researchers increasingly look to them as an alternative energy source. Solar panels are widely used in earth-orbiting satellites and interplanetary spacecraft. The famed Mars rovers could never have worked without them. Some alternative-energy enthusiasts have built systems that use solar panels in conjunction with rechargeable batteries, such as the lead-acid or nickel-cadmium types, to provide power independent of the commercial utilities.
A completely independent solar/battery power system is called a stand-alone system. It employs large solar panels, large-capacity lead-acid batteries, a power inverter to convert the DC into AC, and a sophisticated charging circuit. Obviously, these systems work best in environments where most days are sunny! The maximum deliverable power in full sunlight depends on the surface area of the panel.
Solar cells, either alone or supplemented with rechargeable batteries, can be connected into a home electric system in an interactive arrangement with the electric utilities. When the solar power system can’t provide for the needs of the household all by itself, the utility company can make up for the shortage. Conversely, when the solar power system supplies more than enough for the needs of the home, the utility company can buy the excess energy from the consumer.
Fuel Cells
In the late 1900s, a new type of electrochemical power device, called the fuel cell, emerged. Many scientists and engineers believe that fuel cells hold promise as an alternative energy source to help offset our traditional reliance on coal, oil, and natural gas.
Hydrogen Fuel
The most talked-about fuel cell during the early years of research and development became known as the hydrogen fuel cell. As its name implies, it derives electricity from hydrogen. The hydrogen combines with oxygen (it oxidizes) to form energy and water. The hydrogen fuel cell produces no pollution and no toxic by-products. When a hydrogen fuel cell “runs out of juice,” we need nothing more than a new supply of hydrogen to get it going again; its oxygen comes from the earth’s atmosphere.
Instead of literally burning, the hydrogen in a fuel cell oxidizes in a controlled fashion and at a much lower temperature. The proton exchange membrane (PEM) fuel cell is one of the most widely used. A PEM hydrogen fuel cell generates approximately 0.7 V DC under no-load conditions. In order to obtain higher voltages, we can connect multiple PEM fuel cells in series. A series-connected set of fuel cells technically forms a battery, but engineers call it a stack.
Commercial manufacturers provide fuel-cell stacks in various sizes. A stack having roughly the size and weight of a book-filled travel suitcase can power a subcompact electric car. Smaller cells, called micro fuel cells, can provide DC to run devices that have historically operated from conventional cells and batteries. These include portable radios, lanterns, and notebook computers.
Other Fuels
Fuel cells can use energy sources other than hydrogen. Almost anything that will combine with oxygen to form energy can work. Methanol, a form of alcohol, is easier to transport and store than hydrogen because methanol exists as a liquid at room temperature. Propane powers some fuel cells. It can be stored in tanks for barbecue grills and some rural home heating systems. Still other fuel cells operate from methane, also known as natural gas. Theoretically, any combustible material will work: even oil or gasoline!
Some scientists object to the use of any energy source that employs so-called fossil fuels on which society has acquired a heavy dependence. To some extent we can dismiss these opinions as elitist, but in another sense, we must acknowledge a practical concern: Our planet has a finite supply of fossil fuels, the demand for which will grow for decades to come, especially in developing countries. Today’s exotic energy alternative might become tomorrow’s fuel of choice in the developed nations. The harder we try to make it so, the sooner it can happen.
A Promising Technology
As of this writing, fuel cells have not replaced conventional electrochemical cells and batteries in common applications, mainly because of the high cost. Hydrogen holds the honors as the most abundant and simplest chemical element in the universe, and it produces no toxic by-products when we liberate its stored energy. Hydrogen might, therefore, seem ideal as the choice for use in fuel cells. But storage and transport of hydrogen has proven difficult and expensive, especially for fuel cells and stacks intended for systems not affixed to permanent pipelines.
An interesting scenario, suggested by one of my physics teachers in the 1970s, involves piping hydrogen gas through lines already designed to carry methane. Some infrastructure modification would be necessary to safely handle hydrogen, which escapes through small cracks and openings more easily than methane. But hydrogen, if obtained at reasonable cost and in abundance, could power large fuel-cell stacks in households and businesses. Power inverters could convert the DC from such a stack to utility AC. A typical home power system of this sort would easily fit into a small room or a corner of the basement.
Quiz
Refer to the text in this chapter if necessary. A good score is 18 correct. Answers are in the back of the book.
1. Some interactive solar power systems for residential homes
(a) operate from storage batteries during the day and recharge them at night.
(b) can operate sophisticated systems such as computers, but not simple appliances such as lamps.
(c) operate independently from the electric company.
(d) allow the homeowner to sell energy to the electric company when the solar panels produce more power than the home needs.
2. Fill in the blank to make this statement true: “If you plot a battery discharge graph and see steady current for a while and then a rapid drop, then your battery has a ________ discharge characteristic.”
(a) uniform
(b) flat
(c) logarithmic
(d) linear
3. A rechargeable battery, such as the one that starts your car, comprises
(a) stand-alone cells.
(b) primary cells.
(c) secondary cells.
(d) interactive cells.
4. If all other factors remain constant, then the total energy that an electrochemical battery can produce depends on
(a) its voltage.
(b) the number of cells that it has.
(c) its size and mass.
(d) the brightness of the light striking it.
5. The no-load voltage produced by several identical cells connected in series is
(a) higher than the voltage produced by a single cell.
(b) the same as the voltage produced by a single cell.
(c) lower than the voltage produced by a single cell.
(d) dependent on the current.
6. Under no-load conditions and bright sunlight, the output voltage from a PV cell
(a) attains its maximum possible value.
(b) declines with time.
(c) increases with time.
(d) equals zero.
7. What does a power inverter not do?
(a) Allow household appliances to operate from batteries.
(b) Convert AC to DC.
(c) Convert DC to AC.
(d) Work in solar power systems for home use.
8. Fill in the blank to make the following statement true: “Memory drain sometimes occurs in ________ cells and batteries.”
(a) primary
(b) alkaline
(d) nickel-based
9. We connect five identical cells in parallel. Each individual cell produces 1.5 V under no-load conditions, and can deliver up to 12 A of current with a heavy load. Which of the following characteristics can we expect the whole battery to have?
(a) A no-load voltage of 1.5 V and a maximum deliverable current of 12 A
(b) A no-load voltage of 1.5 V and a maximum deliverable current of 60 A
(c) A no-load voltage of 7.5 V and a maximum deliverable current of 12 A
(d) A no-load voltage of 7.5 V and a maximum deliverable current of 60 A
10. Most automotive batteries contain, among other things,
(a) sulfuric acid.
(b) nickel.
(c) cadmium.
(d) P-type silicon.
11. You have a new 6.3-V lantern battery with an energy storage capacity of 5.2 Ah. If you connect a 63-ohm resistor to the battery but no other load, for how long should you expect current to flow through the resistor?
(a) 31 minutes
(b) 5 hours and 12 minutes
(c) 2 days and 4 hours
(d) 21 days and 16 hours
12. The maximum current that a battery can deliver depends on
(a) its chemical composition.
(b) the number of cells that it has.
(c) its no-load output voltage.
(d) its no-load output power.
13. In a portable lamp that consumes considerable power, you would probably find
(a) a size-AA alkaline cell.
(b) a lantern battery.
(c) a fuel cell.
(d) a PV panel.
14. The maximum power that a silicon PV panel can deliver depends on
(a) its surface area.
(b) the voltage of its cells.
(c) its no-load output voltage.
(d) its no-load output current.
15. Figure 7-3 represents a cell or battery with
(a) nonlinear voltage output.
(b) a nearly ideal discharge characteristic.
(c) poor energy-handling capability.
(d) nonlinear power storage capacity.
16. Fill in the blank to make the following sentence true: “A transistor battery has a voltage equal to that of ________ size AA ‘grocery store’ flashlight cells connected in series.”
(a) three
(b) four
(c) six
(d) nine
17. You have two identical alkaline cells that each produce exactly 1.5 V as long as the current demand remains under 2.0 A. You connect them in series and then place a 1.5 k resistor across the combination. The resistor draws
(a) 0.5 mA of current.
(b) 1.0 mA of current.
(c) 2.0 mA of current.
(d) 4.0 mA of current.
18. You connect the same two cells (those described in the previous question) in parallel and then place a 1.5 k resistor across the combination. The resistor draws a current of
(a) 0.5 mA.
(b) 1.0 mA.
(c) 2.0 mA.
(d) 4.0 mA.
19. You have two identical alkaline cells that each produce 1.5 V as long as the current demand remains under 2.0 A. You connect them in series and then place a 1.5 k resistor across the combination. The resistor dissipates
(a) 1.5 mW of power.
(b) 3.0 mW of power.
(c) 6.0 mW of power.
(d) 12 mW of power.
20. You connect the same two cells (those described in the previous three questions) in parallel and then place a 1.5 k resistor across the combination. The resistor dissipates
(a) 1.5 mW of power.
(b) 3.0 mW of power.
(c) 6.0 mW of power.
(d) 12 mW of power.