Electricity and magnetism (third edition) part 2
➤ Gửi thông báo lỗi ⚠️ Báo cáo tài liệu vi phạmNội dung chi tiết: Electricity and magnetism (third edition) part 2
Electricity and magnetism (third edition) part 2
Alternating-current circuitsOverview In earlier chapters we encountered resistors, capacitors. and inductors. We will now study circuits containing al Electricity and magnetism (third edition) part 2ll three of these elements. If such a circuit contains no emf source, the current takes the form of a decaying oscillation (in the case of small damping). The rate of decay is descnbed by the Q factor. If we add on a sinusoidally oscillating emf source, then the current will reach a steady state wit Electricity and magnetism (third edition) part 2h the same frequency of oscillation as the emf source. However, in general there will be a phase difference between the current and the emf. This phasElectricity and magnetism (third edition) part 2
e, along with the amplitude of the current, can be determined by three methods. The first method is to guess a sinusoidal solution to the differentialAlternating-current circuitsOverview In earlier chapters we encountered resistors, capacitors. and inductors. We will now study circuits containing al Electricity and magnetism (third edition) part 2tual current. The third is to use complex voltages. currents, and impedances. These complex impedances can be combined via the same series and parallel rules that work for resistors. As we will see. the third method is essentially the same as the second method, but with better bookkeeping; this make Electricity and magnetism (third edition) part 2s it far more tractable in the case of complicated circuits. Finally, we derive an expression for the power dissipated in a circuit, which reduces toElectricity and magnetism (third edition) part 2
the familiar V2/R result if the circuit is purely resistive.8.1 A resonant circuitA mass attached to a spring is a familiar example of an oscillator. Alternating-current circuitsOverview In earlier chapters we encountered resistors, capacitors. and inductors. We will now study circuits containing al Electricity and magnetism (third edition) part 2.390Alternating-current circuitsThe F = ma equation for that system is — kx-b.ị = Illi. We can compare this with Eq. (8.2) (after multiplying through by L):L%+R% + a\V = 0 «= 0(8.3)(it- dt \CJdi- dtWe see that the inductance L is the analog of the mass m\ this element provides the inertia that resis Electricity and magnetism (third edition) part 2ts change. The resistance R is the analog of the damping coefficient b: this element causes energy dissipation. And the inverse of the capacitance. IElectricity and magnetism (third edition) part 2
/C. is the analog of the spring constant k: this element provides the restoring force. (There isn't anything too deep about the reciprocal form of 1/CAlternating-current circuitsOverview In earlier chapters we encountered resistors, capacitors. and inductors. We will now study circuits containing al Electricity and magnetism (third edition) part 2fficients. We shall try a solution of the formV(t) = Ae ar cos ait.(8.4)where A. a, and w are constants. (See Problem 8.3 for an explanation of where this form comes from.) The first and second derivatives of this function are.............. ,— =Ae “* - a cosoX -.dt1J“TV =Ae-Electricity and magnetism (third edition) part 2
r Sinox)(8.6)+ -p;COSiiX = 0.This will be satisfied for all t if, and only if. the coefficients of sin ail and cos ox are both zero. That is, we must Alternating-current circuitsOverview In earlier chapters we encountered resistors, capacitors. and inductors. We will now study circuits containing al Electricity and magnetism (third edition) part 2ion requires thata> = —- — a —LC L2 I R2U) = rm — ———LC 4L2Alternating-current circuitsOverview In earlier chapters we encountered resistors, capacitors. and inductors. We will now study circuits containing alGọi ngay
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