Resistance, Reactance and Impedance
Electrical resistance (R) is a measure of the resistance that a material or electric circuit presents to the flow of current, and is defined as the ratio of the voltage (V) applied to the electric current (I) which flows through it. The unit of resistance is the ohm. If the resistance is constant over a wide range of voltage, then Ohm's law (I = V/R) can be used to predict the behavior of any material through which a current flows. This definition holds for both DC and AC circuits. Thus, for a given voltage, materials or circuits with a high resistance will allow a small current relative to a material with a low resistance. At the atomic level, currents are defined as the flow of the valence electrons of atoms through a given material. Resistance in this context results from collisions of electrons with other electrons and atoms. Electrical resistance can also be defined in terms of resistivity, a quantity used to describe the resistance of a wire and expressed as the product of its resistance and its cross-sectional area divided by its length. Resistivity and resistance are temperature-dependent and most materials can be classified according to their resistance temperature coefficient. For example, the resistance of positive temperature coefficient (PTC) wires increases strongly with increasing temperature and they are used for current stabilization purposes. In contrast, the resistance of negative temperature coefficient (NTC) wires decreases with increasing temperature and they are used for voltage control purposes.
Electric circuits, the paths followed by electric current, are either DC or AC circuits. The fact that the voltage of AC current varies sinusoidally with time requires the introduction or modification of the quantities required to take this fact into account. Reactance (X), is such a quantity. It is also a measure of the resistance offered by a material or a circuit to the flow of current, but only when the current is alternating. There are two types of reactance, inductive (X) and capacitive (X). The first is associated with the magnetic field induced around a coil or wire through which AC current flows, also called an inductor. The inductive reactance is a measure of the resistance to the flow of this current and it is proportional to the frequency of the alternating current and to inductance (L), an inductor property arising from Faraday's law, and defined in terms of the electromotive force (emf) generated to oppose a given change in current. The capacitive reactance is associated with the changing electric field between two parallel conducting plates separated by an insulator. This arrangement defines a capacitor, which tends to oppose any voltage change across its conducting plates. The capacitive reactance is a measure of this resistance and is inversely proportional to the frequency of the alternating current and to capacitance (C), a capacitor property equal to the magnitude of the charge stored on each capacitor plate (Q) divided by the voltage applied to the plates.
Because Ohm's law applies only to DC circuits and to resistors in AC circuits, a modified version is used for AC circuits. It is expressed as: I=V/Z where I and V are not maximum values, but rather root-mean-square (rms) or "effective" values of voltage and current. The impedance (Z) is a phase angle, which describes the angle between the current and voltage AC sinusoidal curves.
In a resistor, voltage and current are in phase, so effectively, Z= R. In a capacitor, voltage lags current by 90º, and in an inductor, voltage leads current by 90º. Thus, when an AC circuit includes capacitors or inductors, even though Z is also the ratio of the voltage and current peaks, as is the case for R in the DC formulation of Ohm's law, the I and V peaks are now out-of-phase, that is, they do not occur at the same time. The phase of AC circuits is described by phasor diagrams which represent the circuit phase as a vector in a plane. Zero phase is taken to be the positive x-axis and represents the resistor with in-phase voltage and current. The length of the phasor is directly proportional to the magnitude of the quantity represented, and its angle represents its phase relative to that of the current flowing through the resistor.
Impedance consists of the sum of resistance and reactance contributions. The resistance contribution results from the collisions of the electron-carrying current-with the constituent atoms of the conductor material. The reactance component is an additional resistance to the movement of electric charge resulting from the changing magnetic and electric fields occurring in AC circuits. From the modified Ohm's law, the impedance of a circuit is equal to the voltage measured across the circuit, divided by the maximum value of the current through the circuit (Z = V/I). Impedance, like resistance, is expressed in ohms. The reciprocal of the impedance (1/Z), is called the admittance and is expressed in mho.
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