Alternating Current (AC)

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Transcript Alternating Current (AC)

Warm-up—1/15/14
 What happens when you rotate a coil of conductive
material through a uniform magnetic field (not just
move it linearly)?
Assess. State. 12.2.1 – 12.2.9
Assess. State. 12.3.1 – 12.3.5
Due Friday, 1/16/15
AC Generator
As the ring
rotates within
the magnetic
field, what
happens?
AC generators
 Video 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 voltage
 Flux linkage:
Φ = 𝑁𝐵𝐴𝑐𝑜𝑠(𝜃)
 How is the angle in that equation related to the
rotation of the coil?
𝜃 = 𝜔𝑡
 (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
𝜀 = 𝜔𝑁𝐵𝐴 ∙ 𝑠𝑖𝑛(𝜔𝑡)
 Peak Voltage: the maximum induced emf that is
generated by an AC generator (i.e. coil rotating in a
magnetic field)
Peak Voltage
Peak Current
 We are going to safely assume Ohm’s Law works, so the
peak current (maximum current induced) through a
resistor in an AC circuit is:
𝜀 𝜀0 sin(𝜔𝑡)
𝐼= =
𝑅
𝑅
𝐼 = 𝐼0 sin(𝜔𝑡)
Power in an AC Circuit
 Just like AC voltage and current, not constant with
time:
𝑃 = 𝜀𝐼
𝑃 = 𝜀𝑜 𝐼𝑜 sin 2 𝜔𝑡
 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 Voltage
 Root Mean Square (rms) Voltage and Current:
 The best way we have of measuring an average voltage or
current in AC circuits
 Step 1: Square the Current(or voltage)
𝐼 2 = 𝐼0 2 sin2 𝜔𝑡
2
𝐼
0
𝐼2 =
1 − cos 2𝜔𝑡
2
 Step 2: average this (now always positive) quantity

In 1 cycle, the cosine term averages to zero!
2
𝐼
0
𝐼2 =
2
 Step 3: Take that average’s square root
𝐼𝑟𝑚𝑠 =
Same thing for voltage:
𝜀𝑟𝑚𝑠 =
𝐼0
2
𝜀0
2
Average Power:
𝑷 = 𝜺𝑟𝑚𝑠 𝑰𝑟𝑚𝑠
Transformers
 A 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 coils
 Primary coil the coil that is the “input” to the
transformer

Incoming alternating current generates an ever-changing flux
 Secondary 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--quantified
 The 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
∆Φ
a rate shown by
𝑉𝑝 = 𝑁𝑝
Δ𝑡
 The secondary coil generates an induced emf:
∆Φ
𝑉𝑠 = 𝑁𝑠
Δ𝑡
Transformers--continued

∆Φ
Δ𝑡
is a constant, which leaves us the following ratio:
𝑉𝑝 𝑁𝑝
=
𝑉𝑠 𝑁𝑠
 Knowing that an ideal transformer will have no power
loss between the coils, so 𝐼𝑝 𝑉𝑝 = 𝐼𝑠 𝑉𝑠 , this can also be
written as:
𝐼𝑠 𝑉𝑝 𝑁𝑝
= =
𝐼𝑝 𝑉𝑠 𝑁𝑠
Example:
Step-down and Step-up Transformers
 Step-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 voltage
 More loops in secondary coil