Varying current induces voltage in a conductor, since the expanding and collapsing field of the current is equivalent to flux in motion.
Lenz's law states that the induced voltage produces I that opposes the change in current causing the induction. Inductance, therefore, tends to keep the current from changing.
The ability of a conductor to produce induced voltage across itself when the current varies is its self-inductance, or inductance. The symbol is L, and the unit of inductance is the henry. One henry of inductance allows 1 V to be induced when the current changes at the rate of 1 A/s. For smaller units, 1 mH = 1 x 10-3 H and 1 μH = 1 x 10-6 H.
To calculate self-induced voltage, vL L(di/dt), with v in volts, L in henrys, and di/dt in amperes per second.
Mutual inductance is the ability of varying current in one conductor to induce voltage in another conductor nearby. Its symbol is LM, measured in henrys. <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=jpg::::/sites/dl/free/0072988215/363997/19_05sum.jpg','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (1.0K)</a> where k is the coefficient of coupling between conductors.
A transformer consists of two or more windings with mutual inductance. The primary winding connects to the source voltage; the load resistance is connected across the secondary winding. A separate winding is an isolated secondary. The transformer is used to step up or step down ac voltage.
An autotransformer is a tapped coil, used to step up or step down the primary voltage. There are three leads with one connection common to both the primary and the secondary.
A transformer with an iron core has essentially unity coupling. Therefore, the voltage ratio is the same as the turns ratio: VP/VS = NP/NS.
Assuming 100% efficiency for an iron-core power transformer, the power supplied to the primary equals the power used in the secondary.
The voltage rating of a transformer's secondary is always specified under full load conditions with the rated primary voltage applied. The measured voltage across an unloaded secondary is usually 5 to 10% higher than its rated value.
The current or power rating of a transformer is usually specified only for the secondary windings.
Transformers can be used to reflect a secondary load impedance back into the primary as a new value that is either larger or smaller than its actual value. The primary impedance ZP can be determined using Formula (19–10).
The impedance transforming properties of a transformer make it possible to obtain maximum transfer of power from a generator to a load when the generator and load impedances are not equal. The required turns ratio can be determined using Formula (19–11).
Eddy currents are induced in the iron core of an inductance, causing wasted power that heats the core. Eddy-current losses increase with higher frequencies of alternating current. To reduce eddy currents, the iron core is laminated. Powdered-iron and ferrite cores have minimum eddy-current losses at radio frequencies. Hysteresis also causes power loss.
With no mutual coupling, series inductances are added like series resistances. The equivalent inductance of parallel inductances is calculated by the reciprocal formula, as for parallel resistances.
The magnetic field of an inductance has stored energy ξ = ½LI2. With I in amperes and L in henrys, energy ξ is in joules.
In addition to its inductance, a coil has dc resistance equal to the resistance of the wire in the coil. An open coil has infinitely high resistance.
An open primary in a transformer results in no induced voltage in any of the secondary windings.
Figure 19–34 summarizes the main types of inductors, or coils, with their schematic symbols.
The characteristics of inductance and capacitance are compared in Table 19-1.
Stray inductance can be considered the inductance of any wiring not included in conventional inductors. Stray capacitance can be considered the capacitance of any two conductors separated from each other by an insulator and not included in conventional capacitors.
