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 . $5.00 \times 10^{- 21} H$

Step by step solution

Write the given quantities

Capacitor,

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

Wavelength,

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

Velocity of light

$c = 3 \times 10^{8} \frac{m}{s}$

Determine the concepts of inductance and LC circuit

If f is the frequency and𝛌is 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:

$f = \frac{1}{2 π \sqrt{L C}}$

$f = \frac{c}{λ}$

Determine the inductance of the oscillator

Consider the formula for the frequency as:

$f = \frac{1}{2 π \sqrt{L C}}$

But we know that

$f = \frac{c}{λ}$

Therefore,
$\frac{c}{λ} = \frac{1}{2 π \sqrt{L C}}$

Solving for L,

$L = \frac{λ^{2}}{4 π^{2} C c^{2}}$

Substitute the values and solve as:

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

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

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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

Step by step solution

Write the given quantities

Determine the concepts of inductance and LC circuit

Determine the inductance of the oscillator

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What inductance must be connected to a17pFcapacitor in an oscillator capable of generating550nm(i.e., visible) electromagnetic waves? Comment on your answer.

Short Answer

Step by step solution

Write the given quantities

Determine the concepts of inductance and LC circuit

Determine the inductance of the oscillator

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Wave Optics

Electric Charge Field and Potential

Thermodynamics

Atoms and Radioactivity

Particle Model of Matter

Electricity and Magnetism

Study anywhere. Anytime. Across all devices.

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.