You can boil water in all kinds of ways—even in a simple pan on an open fire or stove—though an enclosed kettle is usually much faster: it stops heat escaping, allows the pressure to rise faster (remember that water boils when its saturated vapor pressure equals atmospheric pressure), and helps the water to boil more quickly. But do you ever get frustrated at how long it takes your kettle to boil? Don't! The amazing thing is that your kettle boils as quickly as it does—and here's why.
If you keep pumping heat energy into the bottom of a kettle (faster than heat is escaping through the top and the sides), sooner or later the water inside it will boil. A basic law of physics called the conservation of energy tells us that if you need to boil a liter of water, starting from the same temperature, you'll always have to add the same amount of energy to do it. Whether you use a camp fire or a kettle, a microwave or some amazing stirring device in the manner of James Prescott Joule, the amount of energy you have to put in to boil the water is exactly the same.
Let's say you start with 1 liter (roughly 1 kilogram, 2.2 lbs) of cold water at about 10°C (50°F) and you want to raise it 90°C to its boiling point (100°C or 212°F). The amount of energy you need is 4.2 × 1000 grams × 90 degrees = 378,000 joules or 378 kJ.
The mysterious "4.2" is a constant value called the specific heat capacity of water. Every material has a different specific heat capacity, which is simply the amount of energy you have to put in to raise the temperature of one gram of the material by one degree centigrade. You need to add 4.2 joules of energy to raise the temperature of 1 gram of water by 1°C, so water's specific heat capacity is 4.2 J/g/°C.
378kJ to boil a liter of water is rather more energy than you might think. An energy-efficient lamp rated at 10 watts uses 10 joules of energy every second (because 1 watt means using one joule per second), so it would take it 37,800 seconds—about 10.5 hours—to use as much energy as our kettle uses in a single boil!
If you're using an electric kettle rated at 2400 watts, that means it's consuming 2400 joules of electrical energy per second and putting (roughly) the same amount of energy into the water as heat each second as well. Divide 378,000 by 2400 and you find it takes the kettle about 160 seconds to do the job, which sounds about right—an electric kettle generally does take about 2–3 minutes to boil. An old proverb says a watched pot (kettle) never boils, but that dates from the time when most people used to boil water on hideously inefficient open coal fires. An electric kettle can boil water in just a couple of minutes because it can add heat energy to the water much more quickly and efficiently than an open fire (which allows heat to escape in all directions).
If your kettle were rated at something like 2400 watts (W) and you were using a UK power supply of 240 volts (V), that means the current passing through the element would be 2400 / 240 or 10 amps (A). By household standards, that's a hefty current: in comparison, the little charger I have for my iPod draws a maximum current of 0.67 amps—the kettle is using 15 times more! So the answer to how an electric kettle works so quickly is by using a relatively large electric current. The amount of heat produced is proportional to the current (a 10 amp current would produce twice as much heat as a 5 amp current passing through the same heating element if the voltage were constant), so bigger currents produce more heat—and heat things much more quickly—than smaller ones.