Simple Nature - Light and Matter

n/Ballasts for fluorescent lights. Top: a big, heavy inductor used as a ballast in an old-fashioned fluorescent bulb. Bottom: a ...

o/An RC circuit. exert mechanical forces on things. Modern compact fluorescent bulbs have ballasts built into their bases that u ...

p/Over a time interval RC, the charge on the capacitor is reduced by a factor ofe. q/An RL circuit. is proportional toq: ifqis l ...

r/Example 29. be very large. First, the air’s resistance is large, soV =IRre- quires a large voltage. We can also reason that al ...

s/Visualizing complex num- bers as points in a plane. t/Addition of complex num- bers is just like addition of vectors, although ...

v/A complex number can be described in terms of its magnitude and argument. w/The argument of uv is the sum of the arguments of ...

x/The complex number eiφ lies on the unit circle. y/Leonhard Euler (1707-1783) in real life, numbers are always approximations a ...

Whenx= iφis imaginary, the quantity (1 +iφ/n) represents a number lying just above 1 in the complex plane. For largen, (1 + iφ/n ...

z/In a capacitor, the current is 90◦ ahead of the voltage in phase. aa/Representing functions with points in polar coordinates. ...

ac/The current through an inductor lags behind the voltage by a phase angle of 90◦. The simplest examples of how to visualize th ...

Similar math (but this time with an integral instead of a deriva- tive) gives ZL=iωL [impedance of an inductor] for an inductor. ...

But for a high-frequency signal, the capacitor’s impedance is very small, and it acts like a zero-impedance, easy path into whic ...

ad/Power in a resistor: the rate at which electrical energy is being converted into heat. radiating light.^7 Since the circuit o ...

The average power is Pav= energy transferred in one full cycle time for one full cycle = IoVoT/ 2 T = IoVo 2 , i.e., the average ...

ae/Power in a capacitor: the rate at which energy is being stored in (+) or removed from (-) the electric field. af/We wish to m ...

so Pav=IoVo/ 2 =Io^2 Zo/ 2 = Vo^2 Zo (Zo+ZT)^2 /2. The maximum of this expression occurs where the derivative is zero, 0 = 1 2 d ...

10.5.10 Impedances in series and parallel How do impedances combine in series and parallel? The beauty of treating them as compl ...

ag/Example 37. A second-order stereo crossover filter example 37 A stereo crossover filter ensures that the high frequencies go ...

10.6 Fields by Gauss’ law 10.6.1 Gauss’ law The flea of subsection 10.3.2 had a long and illustrious scientific career, and we’r ...

a/The area vector is de- fined to be perpendicular to the surface, in the outward direction. Its magnitude tells how much the ar ...