In a parallel hybrid motorized bicycle, such as the aforementioned 1897 invention by Hosea W. Libbey, human and motor inputs are mechanically coupled either in the bottom bracket, the rear or the front wheel, whereas in a (mechanical) series hybrid cycle, the human and motor inputs are coupled through differential gearing. In an (electronic) series hybrid cycle, human power is converted into electricity and is fed directly into the motor and mostly additional electricity is supplied from a battery.
Since fat tire electric bikes are suitable for a wider variety of situations than a standard cruiser or commuter e-bike, they have the potential to appeal to more people. For example, hunters and campers are ideal candidates for fat tire e-bikes, as they’ll benefit greatly from the heavy-duty tires and powerful motor when they’re navigating difficult wooded trails with lots of gear.
Speaking of which, if you're used to non-electric cycles, be aware that e-bikes are heavy and capped at 25kph or 15.5mph. In many cases, that means the bike starts to feel like its actively fighting against you, if you try to push the speed higher than that by pedalling. That's especially true with heavier bikes, for obvious reasons, and can take a while to get used to. 
The bicycle is extraordinarily efficient in both biological and mechanical terms. The bicycle is the most efficient human-powered means of transportation in terms of energy a person must expend to travel a given distance.[38] From a mechanical viewpoint, up to 99% of the energy delivered by the rider into the pedals is transmitted to the wheels, although the use of gearing mechanisms may reduce this by 10–15%.[39][40] In terms of the ratio of cargo weight a bicycle can carry to total weight, it is also an efficient means of cargo transportation.
Geared Hub Motors – Most pre-built e-bikes use brushless geared hub motors. These motors have internal planetary gears that help transfer power from the motor to the wheel. Because of the internal gearing, these motors provide excellent torque but are limited in top speed. On the plus side, the improved torque means better take-off power and hill climbing ability. Plus, less wattage is required to get the motor turning and they’re typically small and lightweight. On pre-built e-bikes, these motors range from 200w-500w and go up to 20mph. But some aftermarket kits can be as powerful as 1000w, with increased top speeds and huge amounts of torque (ideal for extremely hilly terrain). Besides lower top speeds, these motors tend to be expensive and it’s possible the gears will eventually wear out and need to be replaced (this is highly unlikely, they las quite a long time). Good examples are Ancheer bikes.

Under Arizona law, motorized electric bicycles and tricycles meeting the definition under the applicable statute are not subject to title, licensing, insurance, or registration requirements, and may be used upon any roadway authorized for use by conventional bicycles,[77] including use in bike lanes integrated with motor vehicle roadways. Unless specifically prohibited, electric bicycles may be operated on multi-use trails designated for hiking, biking, equestrian, or other non-motorized usage, and upon paths designated for the exclusive use of bicycles. No operator's license is required, but anyone operating a bicycle on Arizona roads must carry proof of identity.[78] A "motorized electric bicycle or tricycle" is legally defined as a bicycle or tricycle that is equipped with a helper motor that may be self-propelled, which is operated at speeds of less than twenty miles per hour. Electric bicycles operated at speeds of twenty miles an hour or more, but less than twenty-five miles per hour may be registered for legal use on the roadways as mopeds, and above twenty-five miles per hour as a registered moped with an 'M' endorsement on the operator's driving license. However, mopeds in Arizona are prohibited from using bike lanes on motor vehicle roadways. The Arizona statute governing motorized electric bicycles does not prohibit local jurisdictions from adopting an ordinance that further regulates or prohibits the operation of motorized electric bicycles or tricycles.[79]

Every person riding a bicycle, electric personal assistive mobility device, electric power-assisted bicycle, moped, or an animal or driving an animal on a highway shall be subject to the provisions of this chapter and shall have all of the rights and duties applicable to the driver of a vehicle, unless the context of the provision clearly indicates otherwise.

The first functioning electric motor was displayed in the early 19th century, though the device constructed by British scientist Michael Faraday did little more than swirl a wire around a magnet when an electric charge was introduced. Still, the concept proved that electricity could do work. Functional electric motors would follow in many forms after that achievement in 1821. Soon scientists and tinkerers around the world, including visionaries such as Nikola Tesla, were experimenting with all manner of electric motors -- some worked with DC power, others with AC. By the end of the century, myriad electric motors had been produced, capable of exerting enough force with enough reliable control that they were practical for use in myriad applications.
The rest of the bike is equally impressive. Integrated lights in the front and the rear run directly off the main battery, so you’re never replacing coin cells or AAA batteries. And the disc brakes give you plenty of stopping power. The 36-volt battery attaches to the down tube and is designed to be easily removed for recharging. A key-lock at the top of the mount ensures that no one can steal your battery if your bike is left in a public place. And a built-in alarm system, activated with a car-like key fob, is ear-splitting enough to keep thieves away altogether. (Miller promises the alarm’s sensitivity is tuned so it shouldn’t go off if the bike is jostled at a public bike rack, but I didn’t have the bike long enough to test this out.)
Pedelec is a European term that generally referred to an electric bicycle that incorporated a torque and/or a speed sensor and/or a power controller that delivered a proportionate level of assist and only ran when the rider pedaled. On the opposite side, a Noped is a term used by the Ministry of Transportation of Ontario for similar type vehicles which do not have pedals or in which the pedals have been removed from their motorized bicycle. Finally, Assist Bicycle is the technical term used to describe such a vehicle and Power-Assisted Bicycle is used in the Canadian Federal Legislation, but is carefully defined to only apply to electric motor assist, and specifically excludes internal combustion engines (though this is not the case in the United States).

Vehicles with an electric power and power of less than 300W are classified as "not a motor vehicle". Such electric bicycles must comply with the same rules as bicycles. You must wear a helmet even on a scooter or bike under 300W. If the power is over 300W or a combustion engine is used it is a "low powered vehicle" and the moped rules apply. Specifically, a drivers license and registration are required.
Generally they are considered vehicles (like motorcycles and pedal cycles), so are subject to the same rules of the road. Regulations may define maximum power output and for electric bikes may or may not require an interlock to prevent use of power when the rider is not pedaling. In some cases regulatory requirements have been complicated by lobbying in respect of the Segway HT.
All classes of electric-assisted bicycles may be operated on a fully controlled limited access highway. Class 1 and 2 electric bicycles can be used on sidewalks, but Class 3 bicycles "may not be used on a sidewalk unless there is no alternative to travel over a sidewalk as part of a bicycle or pedestrian path."[143] Generally a person may not operate an electric-assisted bicycle on a trail that is designated as non-motorized and that has a natural surface, unless otherwise authorized.
Further innovations increased comfort and ushered in a second bicycle craze, the 1890s Golden Age of Bicycles. In 1888, Scotsman John Boyd Dunlop introduced the first practical pneumatic tire, which soon became universal. Willie Hume demonstrated the supremacy of Dunlop's tyres in 1889, winning the tyre's first-ever races in Ireland and then England.[28][29] Soon after, the rear freewheel was developed, enabling the rider to coast. This refinement led to the 1890s invention[30] of coaster brakes. Dérailleur gears and hand-operated Bowden cable-pull brakes were also developed during these years, but were only slowly adopted by casual riders.
Electric bikes are becoming a convenient and fun way to commute around a city, but they can be pricey. The average e-bike can cost $3,000, with some models getting up to $5,000 or more. But these prices are dropping, as new models come onto the market — and if you don’t mind giving up some of the glossier, high-tech features like embedded digital displays, retractable cable locks, and and theft tracking and recovery, you can find a really good quality e-bike for under $1,500.