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Chapter 33: Q5P (page 1001)

What inductance must be connected to a $17 pF$ capacitor in an oscillator capable of generating $550 nm$ (i.e., visible) electromagnetic waves? Comment on your answer.

Short Answer

Expert verified

The inductance of the oscillator is . $5.00 脳 10^{- 21} H$

Step by step solution

01

Write the given quantities

Capacitor,

$\begin{array}{rcl} C & = & 17 pf \\ = & 17 脳 10^{- 12} f \end{array}$

Wavelength,

$\begin{array}{rcl} 位 & = & 550 nm \\ = & 550 脳 10^{- 9} m \end{array}$

Velocity of light

$c = 3 脳 10^{8} \frac{m}{s}$

02

Determine the concepts of inductance and LC circuit

If f is the frequency and饾泴is the wavelength of an electromagnetic wave in the LC circuit of a generator, the value for inductance L is found using the formula for frequency of an LC circuit.

Formula:

$f = \frac{1}{2 蟺 \sqrt{L C}}$

$f = \frac{c}{位}$

03

Determine the inductance of the oscillator

Consider the formula for the frequency as:

$f = \frac{1}{2 蟺 \sqrt{L C}}$

But we know that

$f = \frac{c}{位}$

Therefore,
$\frac{c}{位} = \frac{1}{2 蟺 \sqrt{L C}}$

Solving for L,

$L = \frac{位^{2}}{4 蟺^{2} C c^{2}}$

Substitute the values and solve as:

$\begin{array}{rcl} L & = & \frac{{(550 脳 10^{- 9})}^{2}}{4 脳 {(3.14)}^{2} 脳 (17 脳 10^{- 12}) 脳 {(3 脳 10^{8})}^{2}} \\ = & 5.00 脳 10^{- 21} H \end{array}$

The inductance of the oscillator is $5.00 脳 10^{- 21} H$ .

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Most popular questions from this chapter

The electric component of a beam of polarized light is

$E_{y} = (5.00 V/m) s i n [(1.00 脳 10^{6} m^{- 1}) z + 蝇 t]$ .

(a) Write an expression for the magnetic field component of the wave, including a value for $蝇$ .

What are the (b) wavelength, (c) period, and (d) intensity of this light?

(e) Parallel to which axis does the magnetic field oscillate?

(f) In which region of the electromagnetic spectrum is this wave?

The intensity Iof light from an isotropic point source is determined as a function of distance r from the source. The Figure gives intensity I versus the inverse square of that square r^-2. The vertical axis scale is set by I_s=200 w/m², and the horizontal axis scale is set by r_s^-2 = 8.0 m^-2. What is the power of the source?

Figure:

What is the intensity of a traveling plane electromagnetic wave if $B_{m}$ is $1.0 脳 10^{- 4} T$ ?

In Fig. 33-70, unpolarized light is sent into the system of three polarizing sheets, where the polarizing directions of the first and third sheets are at angles $胃_{1} = 30 掳$ (counter-clockwise) and $胃_{3} = 30 掳$ (clockwise). What fraction of the initial light intensity emerges from the system?

In Figure

(a), a beam of light in a material1is incident on a boundary at an angle $胃_{1} =40掳$ . Some of the light travels through the material 2, and then some of it emerges into the material 3. The two boundaries between the three materials are parallel. The final direction of the beam depends, in part, on the index of refraction $n_{3}$ of the third material. Figure (b) gives the angle of refraction $胃_{3}$ in that material versus $n_{3}$ a range of possible $n_{3}$ values. The vertical axis scale is set by $胃_{3a} =30.0掳$ and $胃_{3b} =50.0掳$ .(a) What is the indexof refraction of material , or is the index impossible to calculate without more information?

(b) What is the index of refraction of material 2, or is the index impossible to calculate without more information?

(c) It $胃_{1}$ is changed to $70 掳$ and the index of refraction of a material 3 is $2.4$ , what is $胃_{3}$ ?

Figure:

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