Simple Nature - Light and Matter

or

|VL|=

∣∣

∣∣LdI

dt

∣∣

∣∣.

In the equation for the inductor, the direction of the voltage drop (plus or minus sign) is such

that the inductor resists the change in current. Although the equation for the voltage across

an inductor follows directly from fundamental arguments concerning the energy stored in the

magnetic field, the result is a surprise: the voltage drop implies the existence of electric fields

which are not created by charges. This is aninduced electric field, discussed in more detail in

the next chapter.

A series LRC circuit exhibitsoscillation, and, if driven by an external voltage, resonates.

TheQof the circuit relates to the resistance value. For largeQ, the resonant frequency is

ω≈

1

√

LC

.

A series RC or RL circuit exhibits exponentialdecay,

q=qoexp

(

−

t

RC

)

or

I=Ioexp

(

−

R

L

t

)

,

and the quantityRCorL/Ris known as the time constant.

When driven by a sinusoidal AC voltage with amplitudeV ̃, a capacitor, resistor, or inductor

responds with a current having amplitude

I ̃=

V ̃

Z

,

where theimpedance,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 is

90 ◦behind. We can represent these phase relationships by defining the impedances as complex

numbers:

ZC=−

i

ωC

ZR=R

ZL=iωL

The arguments of the complex impedances are to be interpreted as phase relationships between

the oscillating voltages and currents. The complex impedances defined in this way combine in

series and parallel according to the same rules as resistances.

When a voltage source is driving a load through a transmission line, the maximum power is

delivered to the load when the impedances of the line and the load are matched.

Gauss’ law states thatfor any region of space, the flux through the surface,

Φ =

∑

Ej·Aj,

1084 Chapter Appendix 5: Summary