CIE IGCSE Physics (0625) A.C. Generator Study Notes - New Syllabus
CIE IGCSE Physics (0625) A.C. Generator Study Notes
LEARNING OBJECTIVE
- Understanding the concepts of A.C. Generator
Key Concepts:
- Simple A.c. Generator – Description and Working
- E.m.f. vs Time for a Simple a.c. Generator
Simple A.c. Generator – Description and Working
Simple A.c. Generator – Description and Working
An a.c. generator converts mechanical energy into alternating electrical energy by electromagnetic induction. A simple generator consists of either a rotating coil in a magnetic field or a rotating magnet near a fixed coil.
- Rotating Coil Model: A rectangular coil rotates between the poles of a permanent magnet.
- Magnetic Field: Provided by two poles of a magnet (north and south).
- Slip Rings: Two metal rings connected to the rotating coil. They rotate with the coil.
- Brushes: Conductive contacts (usually made of carbon) that rest against the slip rings. They transfer the current to the external circuit.
How It Works:
- As the coil rotates in the magnetic field, the magnetic flux linking the coil changes.
- This change induces an e.m.f. in the coil, following Faraday’s Law.
- The direction of the induced e.m.f. changes every half turn, producing an alternating current (a.c.).
- The slip rings allow continuous rotation of the coil while maintaining electrical contact with the external circuit through the brushes.
Example:
Explain why the output from a simple a.c. generator changes direction periodically.
▶️ Answer/Explanation
As the coil rotates in the magnetic field, the magnetic flux through the coil changes with time.
During one half of the rotation, the induced current flows in one direction. In the next half-turn, the direction of the induced e.m.f. reverses, because the sides of the coil now move in the opposite direction through the magnetic field.
This results in an alternating voltage and current, creating an a.c. waveform.
The use of slip rings and brushes ensures continuous and smooth transfer of this alternating signal to the external circuit.
Final Answer:
The output alternates because the direction of the induced e.m.f. reverses every half-turn of the coil.
E.m.f. vs Time for a Simple a.c. Generator
E.m.f. vs Time for a Simple a.c. Generator
In a simple a.c. generator, the coil rotates uniformly in a magnetic field. The induced e.m.f. changes sinusoidally over time as the angle between the coil and magnetic field changes.
- The e.m.f. is maximum when the coil is moving parallel to the magnetic field (cutting magnetic lines at maximum rate).
- The e.m.f. is zero when the coil is moving perpendicular to the field (coil is aligned with the field; rate of change of flux is zero).
- This variation follows a sine wave: \( \text{e.m.f.} = E_{\text{max}} \sin(\omega t) \)
Where \( E_{\text{max}} \) is the maximum e.m.f., \( \omega \) is angular velocity, and \( t \) is time.
Interpretation of Graph:
- At 0°, 180°, 360° → e.m.f. = 0 → Coil is perpendicular to field → no change in magnetic flux.
- At 90° → peak positive e.m.f. → maximum rate of flux cutting → coil is horizontal.
- At 270° → peak negative e.m.f. → coil moves in opposite direction relative to field.
The sinusoidal shape arises from the rotational motion and the sine dependence of the flux change rate.
Example:
A rectangular coil is rotating steadily in a uniform magnetic field and is connected to a load via slip rings. It completes one full rotation every 0.04 seconds. Sketch the graph of the induced e.m.f. against time and explain the meaning of the peaks and zero points on the graph.
▶️ Answer/Explanation
The time for one full rotation is \( T = 0.04 \, \text{s} \), so frequency \( f = \frac{1}{T} = 25 \, \text{Hz} \).
- The coil rotates uniformly, so magnetic flux changes sinusoidally.
- This results in a sinusoidal induced e.m.f.: \( \text{e.m.f.} = E_{\text{max}} \sin(\omega t) \).
- \( \omega = 2\pi f = 2\pi \times 25 = 157.1 \, \text{rad/s} \)
Key Points on the e.m.f. Graph
- At \( t = 0 \): coil is aligned with magnetic field → \( \text{e.m.f.} = 0 \)
- At \( t = 0.01 \, \text{s} \): 90° (1/4 cycle) → \( \text{e.m.f.} = +E_{\text{max}} \)
- At \( t = 0.02 \, \text{s} \): 180° (1/2 cycle) → \( \text{e.m.f.} = 0 \)
- At \( t = 0.03 \, \text{s} \): 270° (3/4 cycle) → \( \text{e.m.f.} = -E_{\text{max}} \)
- At \( t = 0.04 \, \text{s} \): 360° → back to zero
The changing orientation of the coil in the magnetic field causes the rate of change of magnetic flux to vary sinusoidally. Maximum e.m.f. occurs when the coil cuts magnetic field lines at the fastest rate (horizontal position), and zero e.m.f. when it moves parallel to the field (vertical position).
Induced e.m.f. in an a.c. generator varies sinusoidally with time due to uniform coil rotation in a magnetic field. Peaks correspond to maximum flux change; zero crossings occur when flux change is zero.