Chapter 23 Induced EMF (finally)


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    Flux comes from the latin word for "flow"
    Think of a water flume (square pipe) of width w and height h. Area = w x h
    Units for this would be m x m or m^2
    Now add the velocity of the water, which would be in meters/second (m/s)
    Flux would be the area x velocity, or m^2 x m/s
    What units would we have for flow then?
    m^3/s which is really like a volume per second unit...
    Now, imagine holding your hand in this water current: flat hand vs. sideways hand: which has more resistance?

    In electromagnetism, we use B as the velocity part, and area is still the area part:

    Note that the B is the field, A is the area, and cos theta is the angle FROM NORMAL. (like the hand in the water)
    So if theta is 0°, then Cos theta is 1 (max exposed area, think of yourself in a windstorm)


    If the flux changes FOR ANY REASON, this will generate an electric current (flow) in a conductor. N in this case is the number of turns of wire seeing this changing flux.

    n.b. (nota bene): Flux can change by changing the angle, the area exposed, OR the magnitude of the B field.

    Lenz's law: Just like F -ma or Le Chatelier's principle (the law of equilibrium) in chemistry...
    Things resist the change exerted on them:
    F = ma Masses resist a force making them accelerate. If no acceleration, there is no force (remember?)
    Le Chatelier's principle: (look this up)
    Eddy Currents and magnetic damping:
    Generated current is shorted out in the material

    Magnetic stove tops: same deal, they only work with certain cookware (iron or steel, not aluminum)

    Small omega (looks like w) means rotational velocity in radians per second
    Be careful in calculations with this, make sure your calculator us usually set for degrees

    emf = 2Blvsinwt

    But since most generators have many turns of wire, and may have an area we can describe:

    emf = NABwsinwt

    Or, since emfo is NABw,

    emf = emfo sinwt

    This is confusing stuff, since rotation was months ago...
    Recall that:
    t = t
    v = w
    a = alpha
    x = theta in radians

    Much more interesting are transformers:
    If you magnetically couple a coil with another coil, and pass AC through one, it will induce AC current in the second one:

    If the number of turns in the secondary is 2x the turns in the primary, this will be a "step up" transformer, and double the voltage there.
    Since P = iV, if the voltage is 2x, then the current is x/2:

    23.8-Electrical safety
    Grounding: three wire plugs vs. fat one side plugs-why?
    GFI or GFCI plugs-find one, test it out
    How does it work?
    Why will my GFCI outlets all fire if I use my radio transmitter nearby?

    23.9 Inductance
    L is the symbol, inductance is the ability of a coil (inductor) to create a magnetic field.

    The best way to imagine this is to go back to SHM (simple harmonic motion):
    Mass is like the inductor (L)
    Spring constant is like a capacitor (C)
    Friction is like a resistor (R)
    Velocity is like current (i)
    we call these combinations LRC circuits for this reason...

    The energy we can store in a mass-spring system is 1/2kx^2 for the spring part and 1/2mv^2 for the KE part , remember?
    The energy we can store in an inductor is like the 1/2mv^2 part of the spring mass system:

    Inductors in circuits act like a mass in a system: they resist any change in position or velocity (e.g. acceleration)

    Once current stabilizes, inductors (L) act like wires, conducting like a wire.

    Capacitors are the opposite, they act like a broken wire when the current stabilizes (in series).

    When these components are in parallel, they can block or pass AC current (this is how your graphic equalizer works)

    See power supply, graphic equalizer, speaker crossover network, noise filter...

    An AC term involving L and C, ALWAYS dependent on frequency:
    Reactance is like "AC resistance"

    Inductive reactance:

    Note that as f approaches zero (DC), "resistance" becomes zero, like a straight piece of wire.

    Capacitive reactance:

    Note that as f approaches zero (DC), "resistance" becomes infinite, like a broken wire.

    Resistors have no change from DC to AC, regardless of frequency

    If we combine all three of these, we get something called impedance, which you may have seen on speakers or headphones:

    Note that if there is no XL or Xc, the formula becomes Z = R
    There are cool vector diagrams of this you might enjoy online...
    Another way Z = R could be if XL = Xc:

    Do the math on this, and you'll see that:

    Invert this for period:

    Period =
    Does this remind you of a pendulum?

    Mass on a spring?