K323 / 2027
Electromagnetic induction overview

Topic 3 of 5

A simple a.c. generator

A generator uses mechanical motion to keep changing the magnetic field through a coil. In the rotating-coil model, the induced voltage reverses every half-turn, producing alternating output.

Induction depends on change through the coil. A closed external circuit allows the induced e.m.f. to drive current and transfer energy to a load. The mechanical drive supplies this energy.

Keep electrical contact while the coil rotates

Magnetic poles and rotating coil
The poles provide an external field. A mechanical drive turns the coil on an axle, changing its orientation relative to that field.
Two complete slip rings
Each coil end is permanently connected to its own ring. The rings rotate with the coil and remain insulated from one another.
Stationary brushes and load
Each brush maintains sliding contact with one ring and connects it to the external circuit. The coil ends remain distinct while the coil rotates.

A complete circuit at the positive peak

This oblique view shows the coil at one quarter-turn. A and B mark its near ends; the far ends join at the top. Brown arrows show conventional current through the connected load. The teal arrow shows field direction.

Two complete slip rings keep the rotating coil connected to its loadAn oblique view shows a rectangular coil between a north pole on the left and a south pole on the right. The right active side is A and the left active side B. Their far ends are joined by the top crosspiece. The near A end connects to the upper complete slip ring, labelled Ring A. The near B end connects to the separate lower complete ring, labelled Ring B. A stationary brush at the right of Ring A connects to the right terminal of an external resistive load; a brush at the left of Ring B connects to the load's left terminal. At the illustrated quarter-turn, A is positive relative to B. Conventional current travels from far A to near A, through Ring A and its brush, through the load from right to left, through the brush and Ring B, then from near B to far B and back across the far crosspiece. The loop is complete and the two rings never touch. The dashed grey axle is mechanical and electrically insulated from the coil and rings. Each ring remains attached to its own named coil end as everything on the axle rotates. The stationary brushes do not swap ring connections. Dimensions and current-arrow lengths are schematic.Far ends joinedNSFieldA +B -Brush ABrush BRing ARing B+-External load

Two full rings, two separate connections. Ring A always connects to physical end A; Ring B always connects to B. Each stationary brush stays in contact with its own ring.

The dashed grey line is the insulated axle, not a wire. Its projected crossings make no electrical connection. The coil leads are insulated from the axle and from each other.

At this instant the output is A positive relative to B. Half a turn later the same connections carry the opposite current; the slip rings do not rectify it.

This apparatus view is one quarter-turn into the stated cycle. Physical side A is on the right and its near terminal is positive relative to B's near terminal. External current at this instant runs from brush A through the load to brush B.

Slip rings maintain contact; they do not swap the coil ends or make the output one-way. The split-ring commutator in a d.c. motor has a different role: its segments exchange brushes every half-turn.

Connect the orientation to the graph

Use a uniform field directed right, and look along the axle from the near end. The coil turns clockwise. A and B name the same physical sides throughout.

Define the output voltage as the potential of near terminal A relative to near terminal B, written VA - VB. Positive output means A is at the higher potential. This stated connection and rotation fix the graph's signs.

Follow the same A and B through one turn

Look along the axle from the near end. Rotation is clockwise and the field points right in every stage. The circles locate the active sides. The dashed diameter shows the coil-plane orientation in this end view; it is not another wire joining the near ends.

The output reference stays fixed: voltage at A minus voltage at B. Blue arrows show mechanical motion.

1. Start: 0 s

Start: output 0 VA is above the axle and B below. The field through the coil is at an extreme, but is momentarily not changing: the output is zero. The viewpoint is along the axle from the near end, the rotation arrow is clockwise, and a separate field arrow points right. The dashed diameter is only a plane-orientation guide. Both physical wire labels remain attached to their original sides, and the unchanged rings retain the A-minus-B voltage reference.ABField

0 VPlane perpendicular to the field

A is above the axle and B below. The field through the coil is at an extreme, but is momentarily not changing: the output is zero.

2. One quarter-turn: 0.010 s

One quarter-turn: output +6.0 VA is on the right moving down; B is on the left moving up. Near A is positive relative to near B, giving the first positive peak. The viewpoint is along the axle from the near end, the rotation arrow is clockwise, and a separate field arrow points right. The dashed diameter is only a plane-orientation guide. Both physical wire labels remain attached to their original sides, and the unchanged rings retain the A-minus-B voltage reference.ABField

+6.0 VPlane parallel to the field

A is on the right moving down; B is on the left moving up. Near A is positive relative to near B, giving the first positive peak.

3. Half a turn: 0.020 s

Half a turn: output 0 VThe physical sides have exchanged positions: A is below the axle and B above. The output is momentarily zero again. The viewpoint is along the axle from the near end, the rotation arrow is clockwise, and a separate field arrow points right. The dashed diameter is only a plane-orientation guide. Both physical wire labels remain attached to their original sides, and the unchanged rings retain the A-minus-B voltage reference.ABField

0 VPlane perpendicular to the field

The physical sides have exchanged positions: A is below the axle and B above. The output is momentarily zero again.

4. Three quarters of a turn: 0.030 s

Three quarters of a turn: output -6.0 VA is on the left moving up; B is on the right moving down. Near A is now negative relative to near B, giving the negative peak. The viewpoint is along the axle from the near end, the rotation arrow is clockwise, and a separate field arrow points right. The dashed diameter is only a plane-orientation guide. Both physical wire labels remain attached to their original sides, and the unchanged rings retain the A-minus-B voltage reference.ABField

-6.0 VPlane parallel to the field

A is on the left moving up; B is on the right moving down. Near A is now negative relative to near B, giving the negative peak.

5. One complete turn: 0.040 s

One complete turn: output 0 VA is above and B below again. The original orientation has returned after one period, and the next cycle begins. The viewpoint is along the axle from the near end, the rotation arrow is clockwise, and a separate field arrow points right. The dashed diameter is only a plane-orientation guide. Both physical wire labels remain attached to their original sides, and the unchanged rings retain the A-minus-B voltage reference.ABField

0 VPlane perpendicular to the field

A is above and B below again. The original orientation has returned after one period, and the next cycle begins.

The same five instants on a smooth graph

A sinusoidal A-minus-B output with peak six volts and period forty millisecondsThe vertical axis is output voltage at A relative to B, in volts, with labelled values minus six, zero and plus six. The horizontal axis is time in seconds, with evenly spaced ticks at zero, 0.010, 0.020, 0.030 and 0.040. A smooth sine curve begins at zero and rises to plus six volts at 0.010 seconds, falls through zero at 0.020, reaches minus six at 0.030 and returns to zero at 0.040 seconds. These five marked points match the five orientation views. The coil rotates uniformly in the stated uniform-field model; the output is not a steady voltage. These are supplied model values, not laboratory measurements or a national mains supply.Output voltage / V-60+600.0100.0200.0300.040Time / s

Supplied model: uniform rotation in a uniform field, peak output 6.0 V, and one complete turn every 0.040 s. The sign refers to A relative to B throughout.

At the five marked positions, the output is 0, +6.0, 0, -6.0 and 0 V. The full cycle takes 0.040 s. The orientation guide and the smooth voltage-time curve use the same physical A/B labels and terminal convention.

At zero output, the magnetic field itself has not disappeared. At maximum output magnitude, it is the rate of change through the coil that is greatest. Keep the coil's plane distinct from a line drawn perpendicular to that plane.

For the stated uniform field and uniform rotation, sketch a smooth sinusoidal curve through the cycle, with output voltage on the vertical axis and time on the horizontal axis. Straight segments between the five marked points would describe a different waveform.

The period is T = 0.040 s, so the frequency is f = 1/T = 25 Hz. Constant rotation speed does not mean constant output voltage. Swapping the output leads would reverse every voltage sign while leaving the period unchanged.

Change the output under matched conditions

  • Rotate faster: the field through the coil changes faster, so peak voltage increases and the period becomes shorter.
  • Use a stronger field: peak voltage increases for the same coil and rotation speed.
  • Use more turns linked by the changing field: peak voltage increases with the field, coil geometry and rotation speed otherwise comparable.

Changing field strength or turn count does not by itself change the frequency when rotation speed stays fixed.

A rotating magnet is another arrangement

A rotating magnet can change the field through stationary coils and produce alternating output. The stationary coil ends can connect directly to the external circuit, so that arrangement does not need slip rings on those output connections. Slip rings are needed where the chosen design must maintain contact with rotating coil ends.

Optional check A coil rotates uniformly in a uniform magnetic field. At t = 0 its plane is perpendicular to the field. Why is the instantaneous output zero at that position in the stated generator model?
A coil rotates uniformly in a uniform magnetic field. At t = 0 its plane is perpendicular to the field. Why is the instantaneous output zero at that position in the stated generator model?