Chapter 24: Q40PE (page 889)

What capacitance is needed in series with an $800 μH$ inductor to form a circuit that radiates a wavelength of $196 m$ ?

Short Answer

Expert verified

The capacitance is $13.53 p . F .$

Step by step solution

Define wavelength

The distance between two successive crests or troughs of a wave is known as its wavelength.

Evaluate capacitance

The frequency of light and its amplitude is known to be connected by the formula

$f = \frac{c}{λ}$

Where is frequency, is the speed of light, is the wavelength.

Substitute the values in the above equation,

$f = \frac{3 \times 10^{8} m / s}{196 m} = 1.53 \times 10^{6} Hz$

The formula for the relationship between inductance and capacitance and the resonant frequency is

$f = \frac{1}{2 π \sqrt{LC}} C = \frac{1}{4 π^{2} f^{2} L}$

Where L is inductance C is capacitance f is frequency.

Substitute the values in the above equation,

$C = \frac{1}{4 π^{2} \times {(1.53 \times 10^{6} Hz)}^{2} \times (8.00 \times 10^{- 4} H)} = 1.353 \times 10^{- 11} F (\frac{1 pF}{10^{- 12} F}) = 13.53 pF$

Therefore, the capacitance is $13.53 pF .$

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What capacitance is needed in series with an $800 μH$ inductor to form a circuit that radiates a wavelength of $196 m$ ?

Short Answer

Step by step solution

Define wavelength

Evaluate capacitance

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What capacitance is needed in series with an800μH inductor to form a circuit that radiates a wavelength of 196m?

Short Answer

Step by step solution

Define wavelength

Evaluate capacitance

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Nuclear Physics

Fundamentals of Physics

Electric Charge Field and Potential

Fields in Physics

Space Physics

Work Energy and Power

Study anywhere. Anytime. Across all devices.

What capacitance is needed in series with an $800 μH$ inductor to form a circuit that radiates a wavelength of $196 m$ ?