When you pedal a high-tech exercise bicycle, you are probably spinning the rotor of an electric generator. That generator supplies power to a heating filament with an adjustable electrical resistance. How should the bicycle alter that electrical resistance to make pedaling more difficult?

An electric generator is a device that transforms mechanical energy into electrical energy. When you pedal a high-tech exercise bicycle, you are essentially moving the rotor of an electric generator. This rotor spins within a magnetic field, and according to Faraday’s Law of Electromagnetic Induction, it induces an electric current.

The generated electrical energy can then be used to power various devices or components, like a heating filament in our case. The harder you pedal, the more mechanical energy is provided to the generator, resulting in a higher electrical output.

In practical terms, electric generators are widely seen in everyday applications. For example:

• Backup generators for homes or businesses during power outages.
• Power generators in vehicles.
• Small portable generators for camping or outdoor use.

So the next time you pedal your high-tech exercise bike, remember you are using an electric generator to create electricity!

A heating filament is an important component in many electrical devices, responsible for converting electrical energy into heat. When electric current passes through the filament, it encounters resistance, causing it to heat up.

In the context of your exercise bicycle, the heating filament's resistance can be adjusted to change the level of difficulty while pedaling. The filament operates similarly to how a light bulb filament functions: electric current flows through, resistance converts electrical energy into thermal energy, and the filament heats up.

Some common applications of heating filaments include:

• Electric heaters.
• Toasters and ovens.
• Incandescent light bulbs.

By controlling the filament’s resistance, you can effectively manipulate how hard you need to pedal to maintain a certain power output. Higher resistance means less power is generated, hence the generator works harder and pedaling becomes more challenging.

Power output is the amount of electrical power produced by a generator. In mathematical terms, power (\text{P}\text{) is given by the formula:
\[ P = \frac{V^2}{R} \]

where:

• \text{P}\text{) is power.
• \text{V}\text{) is voltage.
• [R} is resistance.

Essentially, this means that for a constant voltage, increasing resistance decreases power output, and vice versa. In the exercise bicycle example, when you increase the resistance of the heating filament, the power output decreases.

Consequently, to produce the same power output, you need to pedal harder. Thus, adjusting the resistance indirectly affects the difficulty of your workout. Higher resistance means you exert more effort to maintain a certain power level, making pedaling more challenging.