Revision summary

Produce and measure an induced e.m.f.

A changing magnetic field through a coil can induce an e.m.f., measured in volts. The change may come from relative magnet/coil motion, a changing nearby current or a rotating coil. A steady magnetic arrangement gives no sustained induced e.m.f.

An open coil can have induced e.m.f.; induced current needs a closed conducting path and depends on its resistance. A high-resistance voltmeter measures terminal voltage with little loading. A galvanometer shows current, whose scale must not be relabelled as voltage.

• Approach and withdrawal of the same pole give opposite polarities with the meter leads fixed.
• Reversing which pole approaches reverses the polarity. Holding it still gives zero after transients settle.
• Faster change, a larger field change in the same time, or more turns linked by that change increase induced e.m.f. under comparable conditions.
• Control path, orientation and motion when comparing. Use a suitable voltage range and fast enough recording to resolve a brief peak. Repetition does not fix inconsistent motion or changed circuit resistance.

Oppose the change

The induced polarity drives a current, when the circuit is closed, whose magnetic effect opposes the change producing it. Viewed from the magnet end:

• N approaches: near face N, anticlockwise current.
• N withdraws: near face S, clockwise current.
• S approaches: near face S, clockwise current.
• S withdraws: near face N, anticlockwise current.

Approach is opposed by repulsion and withdrawal by attraction. The induced field can support a decreasing original field; it does not always oppose the original field itself. External work maintains the changing arrangement and supplies electrical output and losses.

Read the generator cycle

Each rotating coil end stays connected to its own complete slip ring and stationary brush. The rings maintain contact without swapping ends. A rotating magnet with stationary output coils is another arrangement.

For uniform rotation in a uniform field, the output-time curve is sinusoidal. With the stated clockwise rotation, rightward field and output V_A - V_B, the cycle is:

0 and 0.040 s

A above, B below; coil plane perpendicular to field; output 0 V.

0.010 s

A right moving down, B left moving up; plane parallel to field; near A positive; output +6.0 V.

0.020 s

A below, B above; plane perpendicular to field; output 0 V.

0.030 s

A left moving up, B right moving down; plane parallel to field; near A negative; output -6.0 V.

Zero output means zero instantaneous rate of change through the coil, not an absent field. The period is 0.040 s and frequency 25 Hz. Faster rotation increases frequency and peak magnitude; stronger field or more linked turns increases magnitude at fixed rotation speed.

Use the ideal transformer

Changing primary current creates a changing field in the iron core, inducing secondary e.m.f. The windings are insulated, separate circuits. Steady d.c. gives no sustained secondary output after switching transients.

1000:50 turns with 240 V input gives 12.0 V output. A 2.0 A secondary load receives 24 W and requires 0.100 A ideal primary current. Conversely, 200:1000 turns with 12 V input gives 60 V output; at 30 W, the primary/secondary currents are 2.5 A and 0.50 A.

Step-up voltage means more secondary turns. At the same ideal power the secondary current is smaller. Real losses make useful output power lower than input power.

Calculate cable loss with cable quantities

At 10.0 kW received and R = 2.0 ohm, a receiving voltage of 1000 V needs 10.0 A and loses 200 W in the cables. The sending end supplies 1020 V and 10 200 W. At 10 000 V received, current is 1.00 A, cable loss 2.00 W, and the sending end supplies 10 002 V and 10 002 W.

A tenfold voltage increase reduces current tenfold and cable loss one hundredfold at fixed delivered power and cable resistance. Do not substitute load voltage for cable drop, or ignore the difference between sending and receiving power.