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Ideal electrical elements

  1. Jun 8, 2014 #1
    A ideial voltage source has:
    v = v
    i = ?
    R = 0
    L = ?
    C = ?

    ideal current source:
    v = ?
    i = i
    R = 0
    L = ?
    C = ?

    ideal resistor:
    v = R i
    i = 1/R v
    R = R
    L = ?
    C = ?

    ideal inductor:
    v = L i/t
    i = 1/L vt
    R = 0
    L = L
    C = ?

    ideal capacitor:
    v = 1/C it
    i = C v/t
    R = 0
    L = ?
    C = C

    *assuming that v, i, R, L and C, varies linearly (just for simplify...).

    I'd of know the values/definition for where I setted "?".
     
    Last edited: Jun 8, 2014
  2. jcsd
  3. Jun 8, 2014 #2
    Ideal voltage source: I = V/Z, L = 0, C = 0
    Ideal current source: V = IZ, L = 0, C = 0
    Ideal resistor: C = 0, L = 0
    Ideal inductor: C = 0
    Ideal capacitor: L = 0

    The abundance of zeros is what makes these "ideal". Although ideal inductors and capacitors have zero resistance, they have nonzero impedance.
     
  4. Jun 8, 2014 #3

    Born2bwire

    User Avatar
    Science Advisor
    Gold Member

    I would note that an ideal voltage source has zero impedance but the ideal current source has infinite impedance.
     
  5. Jun 8, 2014 #4
    Thanks; it didn't occur to me to mention the impedance of sources.

    EDIT: Also, the resistance of a current source is not necessarily zero. You can easily multiply the current by the voltage to obtain a real, nonzero resistance in a DC circuit.
     
  6. Jun 8, 2014 #5

    Born2bwire

    User Avatar
    Science Advisor
    Gold Member

    Yeah, normally it doesn't come up but it can matter when you wish to find equivalent circuits or calculate time constants. I always had a few students every time who would forget about the source impedance when calculating an RC time constant.
     
  7. Jun 8, 2014 #6
    But an ideal current source has resistance zero, correct!?
     
  8. Jun 8, 2014 #7

    Dale

    Staff: Mentor

    No, an ideal current source has infinite resistance.
     
  9. Jun 8, 2014 #8
    Has more something wrong in my first post?
     
  10. Jun 8, 2014 #9

    Dale

    Staff: Mentor

    Not that I see.
     
  11. Jun 8, 2014 #10
    Is that really an accurate representation when we define R = V/I? This is a genuine question from a student, not a challenge from an arrogant newbie.
     
    Last edited: Jun 8, 2014
  12. Jun 8, 2014 #11

    Dale

    Staff: Mentor

    Yes, it is accurate, but you have to be a little smart about R.

    That definition of R only applies for "Ohmic" situations. I.e. where the I-V curve is a straight line through the origin. In those situations the resistance is the inverse slope of that line. The only time a current source has an I-V curve through the origin is when I=0, and in that case the inverse slope is infinite.

    If you have a "non-Ohmic" situation (i.e. the I-V curve is not a straight line through the origin) then you have to adjust your definition of resistance. Usually you would talk about the differential resistance: dV/dI, which is infinite for a current source.

    A third way that you can talk about the impedance of a current source is by considering a Norton equivalent circuit which models a real current source as an ideal current source in parallel with a source resistance. The real source becomes closer and closer to an ideal source as the source resistance becomes infinite.

    So whether you are talking about Ohmic resistance at I=0, or differential resistance, or Norton equivalent resistance, an ideal current source has infinite resistance.

    The chordal resistance is not infinite for I≠0, but it also not well defined, so it is rarely discussed.
     
  13. Jun 8, 2014 #12
    Thanks. The idea makes conceptual sense, and is clearly the assumption made in finding Norton equivalents. But the definition of resistance just suddenly came to mind when I made my second to last post.

    My old physics book seems to be unorthodox in that it emphasizes that R=V/I is not "Ohm's Law" but rather a straightforward definition that is always true. The author used the term "Ohm's law" to refer to the observation that some materials have a linear I-V curve.

    I've never personally heard an engineer or scientist use the term that way, so I may do well to forget it.
     
  14. Jun 8, 2014 #13

    Dale

    Staff: Mentor

    I don't think that is standard usage, at least not for active devices, however I haven't taken a survey or anything to find out.

    When talking about real current sources the resistance of the source is an important performance characteristic that any owner's manual will mention. It refers to the Norton equivalent resistance. So this real current source has a resistance of 500 MΩ and using the same meaning an ideal current source has infinite resistance.
     
    Last edited: Jun 8, 2014
  15. Jun 9, 2014 #14
    Actually, the current of the ideal voltage source is not computed by:
    8a89f7d3622fc859d3bc910a8691b9e9.png

    and the voltage of the ideal current source is not computed by:
    8383fa6312eb5e0b7befb1b4172ae749.png

    ?

    *source: http://en.wikipedia.org/wiki/Harmonic_oscillators#Equivalent_systems
     
  16. Jun 9, 2014 #15
    V=IZ is always true. You only use convoluted equations like those in systems where V and I vary with time and you cannot easily find a solution to V=IZ.

    Most circuits are not harmonic oscillators, though.
     
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