C
CraftExam
medium difficulty10 min

AC Generator and Sinusoidal EMF

An AC generator is a device that converts mechanical energy into electrical energy by rotating a coil in a magnetic field, producing an alternating emf.

In one line: Rotating coil changes flux rhythmically, so generator emf rises, falls, and reverses.

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Understand it

As the coil rotates, the magnetic flux linked with it changes continuously. If the coil has N turns and area A rotating with angular speed ω in a uniform magnetic field B, flux linkage varies with time and the induced emf is sinusoidal: epsilon = NBA ω sin ω t, depending on the chosen starting position.

Example

In a simple AC generator, a rectangular coil rotates between magnetic pole pieces. Slip rings and brushes connect the rotating coil to an external circuit, so the output current alternates direction every half rotation.

Formula and rule

Formula: epsilon = NBA ω sin ω t.

Here epsilon is instantaneous induced emf in volt (V), N is number of turns in the coil, B is uniform magnetic field in tesla (T), A is area of each turn in square metre (m2), ω is angular speed in radian per second (rad s−1), and t is time in second (s).

Maximum emf is ε0 = NBA ω, so epsilon = ε0 sin ω t.

This relation applies to a coil rotating uniformly in a uniform magnetic field with flux changing sinusoidally.

See it worked out

Follow the example line by line, then use the same method on new questions.

Worked example

A generator coil has 100 turns, area 0.020 m2, and rotates at angular speed 50 rad s−1 in a magnetic field of 0.30 T.

  1. 1Maximum emf ε0 = NBA ω = 100 × 0.30 × 0.020 × 50 = 30 V.
  2. 2Therefore, the output emf varies between +30 V and -30 V sinusoidally.

Method you can reuse

  1. 1State the principle of electromagnetic induction.
  2. 2Write flux linkage for the rotating coil.
  3. 3Differentiate flux with respect to time to get induced emf.
  4. 4Identify maximum emf as NBA ω.
  5. 5Explain the role of slip rings and brushes in taking output to the external circuit.

Sketch it in your answer

Draw a rectangular coil between N and S pole pieces, connected to two slip rings, carbon brushes, and an external load. Show axis of rotation, direction of rotation, magnetic field direction, and output terminals.

Check yourself

Answer the question in your head before opening the answer.

Try it yourself

Why is the output of a simple AC generator alternating?

Think first, then show answer
The output is alternating because the rotating coil changes its orientation in the magnetic field every half turn. The direction of change of flux reverses periodically, so the induced emf and current also reverse periodically.

Common wrong answer

Writing constant emf for a rotating coil, missing the factor N, or saying slip rings convert AC into DC.

Don't mix this up

Students often confuse slip rings with split rings. An AC generator uses slip rings to maintain alternating output, while a split-ring commutator is associated with DC output in school-level treatment.

Exam tip

In diagram answers, label coil, magnetic poles, axle, slip rings, brushes, and external load. Also state the energy conversion and the reason for alternating emf.

Write it in the exam

Each point is worth about one mark. Write point 1 for a 1-mark question and keep adding points as the marks go up.

How CBSE asks it

It is asked as labelled diagram, principle of working, derivation of sinusoidal emf, difference between AC and DC generator parts, and maximum emf numericals.
  1. 1

    Enough for 1 mark

    An AC generator is a device that converts mechanical energy into electrical energy by rotating a coil in a magnetic field, producing an alternating emf.

  2. 2

    Add for 2 marks

    Example: In a simple AC generator, a rectangular coil rotates between magnetic pole pieces. Slip rings and brushes connect the rotating coil to an external circuit, so the output current alternates direction every half rotation.

  3. 3

    Add for 3 marks

    As the coil rotates, the magnetic flux linked with it changes continuously.

Practice

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