Warm-up—1/15/14What happens when you rotate a coil of

conductive material through a uniform magnetic field (not just move it linearly)?

Alternating Current (AC)Assess. State. 12.2.1 – 12.2.9Assess. State. 12.3.1 – 12.3.5

Due Friday, 1/16/15

AC GeneratorAs the ring rotates within the magnetic field, what happens?

AC generatorsVideo link (it’s old…and if you watch the

whole thing, it’s long, but it’s good)—we’re just going to watch the first few minutes today

http://www.youtube.com/watch?v=LisefA_YuVg&safe=active

In a nutshell…DC generators—use a split-ring commutator

to ensure that the direction of the induced emf (and resulting current) is always in the same direction upon output from the generator

AC generators—use a set of slip rings to provide constant contact with the brushes, resulting in an induced emf and current that are alternating in magnitude and in direction

Peak voltageFlux linkage:

How is the angle in that equation related to the rotation of the coil?

(at some time, t, the angle of the coil in the magnetic field is q, which depends on how quickly the coil is rotating)

So…a little use of Faraday’s Law, and a little calculus later…

Peak Voltage

Peak Voltage: the maximum induced emf that is generated by an AC generator (i.e. coil rotating in a magnetic field)

Peak Voltage

Peak CurrentWe are going to safely assume Ohm’s Law

works, so the peak current (maximum current induced) through a resistor in an AC circuit is:

Power in an AC CircuitJust like AC voltage and current, not constant

with time:

Peak Power is the product of peak voltage and peak current

Power is always a positive value, and will be equal to zero Watts every half rotation of the coil.

Average power is ½ the peak power:

rms VoltageRoot Mean Square (rms) Voltage and

Current:The best way we have of measuring an average

voltage or current in AC circuitsStep 1: Square the Current(or voltage)

Step 2: average this (now always positive) quantity In 1 cycle, the cosine term averages to zero!

Step 3: Take that average’s square root

Same thing for voltage:

Average Power:

TransformersA tool used to take advantage of the fact that

an alternating current generates an alternating magnetic flux in a coil.

An iron core connects two separate coilsPrimary coil the coil that is the “input” to the

transformer Incoming alternating current generates an ever-

changing fluxSecondary coil the coil that delivers the

“output” Because of the iron core, the flux from the primary

coil induces an emf in the secondary coil and, therefore, a current

Transformers--quantifiedThe induced emf in the secondary coil, as

well as the amount of magnetic flux rate of change is dependent on Faraday’s Law.

The primary coil generates a magnetic flux changing at a rate shown by

The secondary coil generates an induced emf:

Transformers--continued is a constant, which leaves us the following

ratio:

Knowing that an ideal transformer will have no power loss between the coils, so , this can also be written as:

Example:

Step-down and Step-up TransformersStep-Down:

A transformer designed to have a high input voltage and a low output voltage

There will be fewer loops in the secondary coil

Step-up:A transformer designed to have a low input

voltage and a higher output voltageMore loops in secondary coil