Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

What does negative impedance mean?

  1. Feb 17, 2014 #1
    I could see that capacitor impedance is mostly negative.

    Does the negative sign has any significant meaning?

    Also why do people convert impedance to admittance for circuit calculation?

    Please help!
  2. jcsd
  3. Feb 17, 2014 #2
    The capacitor has a negative reactance. Why? Because capacitor voltage lags capacitor current by 90 degrees.
    On the other hand the coil has a positive reactance because coil current is lags the coil voltage by 90 degree.
    As for impedance vs admittance, sometimes the math is easier when we use admittance instead of impedance.
  4. Feb 17, 2014 #3


    User Avatar
    Gold Member

    I assume you are talking about something such as, -jXc or -jXL? the negative is attached to the 'j'. j is a place holder which rotates a vector by ninety degrees, a negative j means that the vector is at negative ninety degrees with respect to some reference phasor (most usually the voltage).

    *off topic* Negative resistance is actually a different phenomenon where a increase in current can actually cause a decrease in voltage across an element. This occurs in some types of gases and is a common reason for ballasts in lighting fixtures.
  5. Feb 21, 2014 #4


    User Avatar
    Gold Member

    To follow up, the negative in this case simply means the opposite just like in math.

    If you are just talking about the negative, you are talking about 180 degrees off its non negative vector.

    Inductive KVARS are in the positive part of the y axis.
    However, inductive current lags the voltage in the negative part of the y axis. They are complex conjugates.

    Capacitive KVARS are in the negative part of the y axis.
    However, capacitive current leads the voltage in the positive part of y axis. Also complex conjugates.

    Imedance in general is defined as R + Jx
    R= 0 in each ideal case below. x is defined as the reactance if memory serves.

    Impedance of inductor is JwL. wL equals x in this case.
    V=IR....so when finding current you divide by that J putting you in the negative y axis as stated above.
    So R(0) + JwL is impedance of inductor. (wL) is the reactance.

    Impedence of capacitor is 1/(JwC).....or you could say -J/(1/wC)...or J*(-1/wC)
    So when finding current, you end up in positive side of y.
    So R(0) + J*(-1/wC) is the impedance of the capacitor. -1/(wC) is the reactance.

    Keep in mind also, that in simple terms J= 1>90. A vector with magnitude of 1 sitting at 90 degrees.
    -J would then mean 1>-90. A vector with magnitude of 1 sitting at -90 degrees.

    Hope that helps a bit.
    Last edited: Feb 21, 2014
  6. Feb 21, 2014 #5

    jim hardy

    User Avatar
    Science Advisor
    Gold Member

    Let's try a gross oversimplification:::

    Think for a moment of a compass rose - North, East, South and West.

    One could think of South as Negative North, and West as Negative East.

    So the negative sign just helps us define something about the capacitor's particular type of impedance.
    I know, that sounds crazy - but bear with me-----

    What's impedance?
    Opposition to current flow.
    Impedance comes in three flavors:
    Resistive, which converts the energy of the flowing current into heat which leaves the circuit;
    Inductive, which stores the energy of the flowing current in a magnetic field for later release back into the circuit;
    Capacitive, which stores the energy of the flowing current in an electric field for later release back into the circuit.

    Now, Inductive and Capacitive impedance are both called Reactive because they both keep the energy in electromagnetic form where it can be recovered, unlike resistive which turns it into heat. In other words there'll be a RE-coverable-ACTIon.

    It so happens that when you start dealing with sine waves, you can graph impedances as if on a map- Resistive points North-South, reactive points East-West. So inductive and capacitive have opposite sign, one is east the other west.
    Resistive can also have a negative sign, but negative resistance is so rare we don't often think of it except in odd devices like tunnel diodes and thyratrons..
    But capacitive and inductive are very real in everyday life.

    Earlier posts gave good descriptions of the arithmetic, i tried to go back another step, for my pea-brain has to 'feel' something before it'll believe the math..

    Was this any help?

    It is VERY IMPORTANT that you work all your homework problems and become fluent in vector notation, rotating phasors and that complex operator-j arithmetic.

    old jim
    Last edited: Feb 21, 2014
  7. Feb 21, 2014 #6


    User Avatar
    Science Advisor
    Homework Helper

    hi nomisme! :smile:
    in AC, you find the impedance by replacing d/dt by jω

    so for a capacitor dV/dt = I/C becomes jωV = I/C, or V = -jωI/C …

    voltage lags current :wink:

    (for an inductor V = LdI/dt becomes V = jωLI … the "j" was on the other side of the equation)
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook