Simple Nature - Light and Matter

or|V L | =∣ LdIdt ∣ .In the equation for the inductor, the direction of the voltage drop (plus or minus sign) is suchthat the inductor resists the change in current. Although the equation for the voltage acrossan inductor follows directly from fundamental arguments concerning the energy stored in themagnetic field, the result is a surprise: the voltage drop implies the existence of electric fieldswhich are not created by charges. This is an induced electric field, discussed in more detail inthe next chapter.A series LRC circuit exhibits oscillation, and, if driven by an external voltage, resonates.The Q of the circuit relates to the resistance value. For large Q, the resonant frequency isω ≈ 1 √LC.A series RC or RL circuit exhibits exponential decay,(q = q o exp − t )RCorI = I o exp(− R )L t,and the quantity RC or L/R is known as the time constant.When driven by a sinusoidal AC voltage with amplitude Ṽ , a capacitor, resistor, or inductorresponds with a current having amplitudeĨ = ṼZwhere the impedance, Z, is a frequency-dependent quantity having units of ohms. In a capacitor,the current has a phase that is 90 ◦ ahead of the voltage, while in an inductor the current is90 ◦ behind. We can represent these phase relationships by defining the impedances as complexnumbers:Z C = − iωCZ R = RZ L = iωLThe arguments of the complex impedances are to be interpreted as phase relationships betweenthe oscillating voltages and currents. The complex impedances defined in this way combine inseries and parallel according to the same rules as resistances.When a voltage source is driving a load through a transmission line, the maximum power isdelivered to the load when the impedances of the line and the load are matched.Gauss’ law states that for any region of space, the flux through the surface,Φ = ∑ E j · A j ,,959