The answer is yes, but the method may not be what you had in mind. While it's possible to make a battery by inserting two dissimilar metal strips into the fruit, the battery that results is really powered by the metals themselves. The fruit juice just acts as an "electrolyte"—an electrically conductive liquid that facilitates the movement of electric charges. Claiming that the fruit is responsible for the energy is like claiming that the stone in "stone soup" (an old tale about a beggar who tricks the villagers in a community into contributing vegetables to spice up the soup that he's making with his magic stone) is really the basis for the soup.
The best way to obtain energy from the fruit is to eat it! The sugars and starches in the fruit have plenty of chemical potential energy that's released when those chemicals are oxidized in your body. This released energy is what allows you to live, work, and play.
An alternator is a device that uses rotary motion to generate electricity. As the car engine turns, it spins a magnet (the rotor) in the alternator and this spinning magnet induces electric currents in a set of stationary wire coils (the stator). The alternator's ability to generate electric currents by spinning a magnet past stationary wires is an example of electromagnetic induction. Induction is a general phenomenon in which a moving or changing magnetic field creates an electric field, which in turn pushes electric charges through a conducting material. Overall, some of the engine's mechanical energy is converted into electric energy.
The amount of energy given to each electric charge that flows through the wires in the stator depends on the speed with which the magnet turns and the strength of that magnet. Whether it's internal or external, the voltage regulator monitors this energy per charge—also known as the voltage—to make sure that it's correct. If not, it adjusts the strength of the alternator's magnet. It can do this because the alternator's magnet is actually an electromagnet and its strength depends on how much current is flowing through its wire coils. The voltage regulator carefully adjusts the current flowing through the electromagnet in order to obtain the proper output voltage from the alternator. Actually, the alternator itself produces alternating current, so a set of solid-state diodes converts this alternating current into direct current. A car's electric system, particularly its battery, operates on direct current. Since the alternator's operation is the same whether the voltage regulator is inside it or external to it, neither version should be better than the other.
By "waterpower" I assume that you mean hydroelectric power. In that case, water from an elevated source enters a pipe and travels downhill to a generating plant. As the water descends, its gravitational potential energy (the stored energy associated with height and the earth's gravity) becomes pressure potential energy (the stored energy associated with pressure) and kinetic energy (the energy of motion). By the time the water reaches the generating plant, it has enormous pressure and a modest speed.
This moving, high-pressure water is then sent through a fan-like turbine. As the water moves toward the low pressure beyond the turbine, it does work on the turbine's rotating blades and its energy is transferred to those blades. The water gives up its energy and the turbine takes away this energy in its rotary motion. The turbine is attached to an electric generator, which uses moving magnets and wire coils to turn the turbine's rotary energy into electric energy. The electric energy is carried away on wire to be used elsewhere. Overall, the water's gravitational potential energy has become electric energy.
You can make electricity by moving a magnet past a wire. The magnet has a magnetic field around it—something that exerts forces on magnetic poles. If you move the magnet and its magnetic field, you create an electric field—something that exerts forces on electric charges. That's because whenever a magnetic field changes with time, it creates an electric field. This electric field will push on the mobile electrons in a wire. So when you move a magnet past a wire, you are producing a changing magnetic field in the wire. This changing magnetic field produces an electric field and the electric field makes the electrons in the wire accelerate. The moving electrons are electricity. Generators move magnets past wires (or wires past magnets) to produce electricity.
In a steam generating plant, water is boiled in a confined container (a "boiler") to produce very high-pressure steam. This steam is allowed to flow through a turbine to the low-pressure region beyond the turbine. A turbine resembles a fan, but one that is turned by the gas that flows through it rather than by a motor. The steam flows through the blades of the turbine and exerts forces on those blades to keep the turbine rotating. The steam loses energy as it twists the turbine around in a circle and this energy is transferred to the rotating turbine. The low-pressure steam is recovered from the end of the turbine. It is then condensed back into liquid water with the help of a cooling tower and then returned to the boiler for reuse.
The rotating turbine is connected to the rotating portion of a generator. This rotating component is an electromagnet and, as it spins, its magnetic field passes across a set of stationary wire coils. Whenever the magnetic field through a coil of wire changes, any current flowing through that coil experiences forces that may add or subtract energy from it. In this case, the rotating magnet transfers energy to the current passing through the wire coils and "generates" electricity. The current in these stationary wires carries away energy from the generator and it is this energy that eventually arrives in your home through the power lines. Overall, the energy flows from the boiler, to the steam, to the turbine, to the generator, to the current, and to your home.
If you are trying to light a 60 watt bulb, you must deliver 60 watts of electric power to it (unless you are willing to have it glow relatively dimly). So the answers to your questions are 60 watts of waterpower and 60 watts of windpower. But you are probably more interested in how much water or wind is needed to run those power sources. An efficient water generator that produces 60 watts of power lowers about 6 liters (or one and a half gallons) of water about 1 meter (or 3 feet) each second. An efficient wind generator that produces 60 watts of power stops about 1 cubic meter (or 32 cubic feet) of air moving at 36 km/h (or 21 mph) each second. Finally, a solar powered vehicle needs at least several hundred watts of power to operate. Since solar panels are only about 20% energy efficient and artificial light sources are also only about 10 to 50% energy efficient, it would take thousands of watts of artificial lighting to operate a solar powered car. Not very practical.
Those three items, electric fields, magnetic fields, and currents, are strongly interrelated. Here are some of those relationships: (1) currents cause magnetic fields, (2) currents that change with time cause magnetic fields that change with time, (3) magnetic fields that change with time cause electric fields, (4) electric fields cause currents to flow in electric conductors. From these relationships, you can see that any time you have a changing current through one circuit, you can end up with a current flowing through another nearby circuit. Power moves from the first circuit to the second circuit with the help of a magnetic field and an electric field. A moving magnet also produces a magnetic field that changes with time and it can send a current through a nearby circuit, too.
Solar cells are made in the same way that semiconductor diodes are made. Two different types of semiconductor, p-type and n-type, are joined together to form a diode—a one-way device for electric current. When light energy is absorbed in the n-type portion of the diode, it can propel an electron across the p-n junction between the materials and into the p-type material. Since the electron can't return across the p-n junction to its original location, it must flow through an external circuit to get back. Since it obtains energy from the light that sent it across the junction, the electron can provide that energy to the circuit. The solar cell is thus a source of electric power.
First, you would need to put enough solar panels in series to develop a voltage greater than that of your battery. For example, to recharge a 1.5 volt battery, you would probably have to attach three or four simple solar cells in series because each one only provides a current passing through it with about 0.5 volts of voltage rise. Having assembled enough solar cells, you should then attach the positive output terminal of the solar cell chain to the positive terminal of your battery and attach the negative output terminal of the solar cell chain to the negative terminal of your battery. When you put the solar cells in the light, they will begin to push electric current backward through the battery and the battery will recharge. Whenever you send current backward through a battery, its electrochemical reactions can run backward and it can recharge to some extent. Unfortunately, some batteries recharge more effectively than others—the bad ones just turn the recharging energy into thermal energy. The only real subtlety in this business is in stopping the charging when the battery is fully recharged. You should check the battery voltage periodically and when it's close to the voltage of a new battery, it probably can't take any more charging.
First, it doesn't matter when the magnet moves past the coils or the coils past the magnet; a generator will work the same way in either case. The voltage produced by the generator is determined by the number of turns in its coils, the strength of its magnet, and the rate at which its magnet turns. The more turns in the coils, the more work the generator does on each charge that passes through those coils and the more voltage the charges have when they leave the generator. The current that the generator can handle is limited by the power of its engine and by the wire's ability to handle the current without wasting too much power. In general, a generator's wire gauge is chosen to minimize power loss while keeping the coils reasonably small and light. If you try to send too much current through the generator, its engine may stall or its wires may overheat.
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