Generator Examples in Physics

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Generator.

This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Physics.

Concept Recap

A device that converts mechanical (kinetic) energy into electrical energy by rotating a coil of wire within a magnetic field, exploiting electromagnetic induction.

Spin a loop of wire between magnets and you get electricity — the changing flux induces a voltage that drives current through an external circuit.

Read the full concept explanation →

How to Use These Examples

  • Read the first worked example with the solution open so the structure is clear.
  • Try the practice problems before revealing each solution.
  • Use the related concepts and background knowledge badges if you feel stuck.

What to Focus On

Core idea: Generators are the reverse of motors — mechanical rotation becomes electrical current through Faraday's law.

Common stuck point: A generator produces alternating current (AC) naturally because the flux through the coil oscillates as it rotates.

Sense of Study hint: When analysing a generator, identify the number of turns N, the magnetic field B, the coil area A, and the angular speed \omega. The maximum (peak) EMF is \mathcal{E}_0 = NBA\omega. The output varies sinusoidally: \mathcal{E} = \mathcal{E}_0 \sin(\omega t). To find RMS voltage, divide the peak by \sqrt{2}.

Worked Examples

Example 1

easy
A simple AC generator has a coil of 50 turns, area 0.04 \text{ m}^2, rotating in a 0.5 \text{ T} magnetic field. What is the peak EMF if the coil rotates at 60 \text{ Hz}?

Solution

  1. 1
    Peak EMF for a generator: \mathcal{E}_0 = NAB\omega, where \omega = 2\pi f.
  2. 2
    Angular frequency: \omega = 2\pi \times 60 = 377 \text{ rad/s}.
  3. 3
    \mathcal{E}_0 = 50 \times 0.04 \times 0.5 \times 377 = 377 \text{ V}

Answer

\mathcal{E}_0 = 377 \text{ V}
An AC generator converts mechanical energy to electrical energy by rotating a coil in a magnetic field. The peak EMF increases with more turns, larger area, stronger field, and faster rotation.

Example 2

medium
A generator produces a peak EMF of 170 \text{ V} at 50 \text{ Hz}. What is the RMS voltage? What frequency is used in the power grid in most countries?

Practice Problems

Try these problems on your own first, then open the solution to compare your method.

Example 1

medium
A generator coil has 100 turns and area 0.05 \text{ m}^2 in a 0.4 \text{ T} field. It needs to produce a peak EMF of 500 \text{ V}. At what frequency must it rotate?

Example 2

hard
A hydroelectric generator produces 10 \text{ MW} at 20{,}000 \text{ V} RMS. What RMS current does it deliver? If the transmission line has 2 \text{ } \Omega resistance, what percentage of power is lost in transmission?
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Background Knowledge

These ideas may be useful before you work through the harder examples.

faradays lawlenzs law