Impedance is defined as the frequency domain ratio of the voltage to the current. In other words, it is the voltage–current ratio for a single complex exponential at a particular frequency ω. In general, impedance will be a complex number, with the same units as resistance, for which the SI unit is the ohm (Ω). For a sinusoidal current or voltage input, the polar form of the complex impedance relates the amplitude and phase of the voltage and current. In particular,
Opposition that a circuit presents to electric current. It includes both resistance and reactance. Resistance arises from collisions of the current-carrying charged particles with the internal structure of the conductor. Reactance is an additional opposition to the movement of electric charge that arises from the changing electric and magnetic fields in circuits carrying alternating current. Impedance in circuits carrying steady direct currents is simply resistance. The magnitude of the impedance Z of a circuit is equal to the maximum value of the potential difference, or voltage V, across the circuit, divided by the maximum value of the current I through the circuit, or simply Z = V/I. The unit of impedance is the ohm.
The units of resistance are Volts / Ampères, or Ohms (). Thus, for a given potential difference, materials with a high resistance will allow a small current relative to a material with a low resistance. In analogy with heat resistance and conductivity, one can define an electrical conductivity as being proportional to the inverse of the resistance. Thus, good electrical conductors, such as copper, have a low resistance, and poor electrical conductors, such as concrete, have a high resistance.
There is another important property that can be measured in electrical systems. This is resistance, which is measured in units called ohms. Resistance is a term that describes the forces that oppose the flow of electron current in a conductor. All materials naturally contain some resistance to the flow of electron current. We have not found a way to make conductors that do not have some resistance.
In the reactance equation, the term “2Ï€f” (everything on the right-hand side except the L) has a special meaning unto itself. It is the number of radians per second that the alternating current is “rotating” at, if you imagine one cycle of AC to represent a full circle's rotation. A radian is a unit of angular measurement: there are 2Ï€ radians in one full circle, just as there are 360o in a full circle. If the alternator producing the AC is a double-pole unit, it will produce one cycle for every full turn of shaft rotation, which is every 2Ï€ radians, or 360o. If this constant of 2Ï€ is multiplied by frequency in Hertz (cycles per second), the result will be a figure in radians per second, known as the angular velocity of the AC system.
IThis might be a good place to recall what you learned about phase in chapter 1. When two things are in step, going through a cycle together, falling together and rising together, they are in phase. When they are out of phase, the angle of lead or lag-the number of electrical degrees by which one of the values leads or lags the other-is a measure of the amount they are out of step. The time it takes the current in an inductor to build up to maximum and to fall to zero is important for another reason. It helps illustrate a very useful characteristic of inductive circuits-the current through the inductor always lags the voltage across the inductor.
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