An AM station is broadcasting a radio wave whose frequency is 1400 kHz.

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Homework Help Overview

The problem involves determining the inductance required for tuning into a radio station broadcasting at a frequency of 1400 kHz, with given capacitance values. The context is within the subject area of electrical circuits, specifically focusing on LC circuits.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants explore the relationship between frequency, inductance, and capacitance in LC circuits. Some question the appropriate formulas to use, while others provide specific equations for calculating inductance based on the given frequency and capacitance values.

Discussion Status

The discussion includes various approaches to calculating inductance, with some participants providing formulas and others attempting to derive values based on the provided information. There is no explicit consensus, but several viable methods are being explored.

Contextual Notes

Participants note the conversion of units, such as capacitance from farads to picofarads and frequency from kilohertz to megahertz, as part of the problem setup. There is also mention of the need for realistic component values in the calculations.

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Homework Statement


An AM station is broadcasting a radio wave whose frequency is 1400 kHz. The value of the capacitance in Figure 24.5 is 8.4 X10 -11 F. The Value of the capacitance in Figure 24.4 is 8.4X10-11 F. What must be the value of the inductance in order that this station can be tuned in the radio?


Homework Equations


c = f(wavelength)
S = cu

The Attempt at a Solution


but I'm not sure the fomula and i don't know how to get it
 
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What is the natural frequency of an LC circuit oscillation?
 
f=1400 Khz
w= 2*pi*f

The natural frequency of an LC circuit is w=(L*C)^(1/2);
solving for L and plugging in the values L=1.5385*10^-10 Henries
 
There is a simple formula for use at radio frequencies, that uses realistic component values.

It is

L = 25330.3 / (F * F * C)

where L is in uH
C is in pF
F is in MHz

8.4 X10 -11 F is 84 pF
1400 KHz is 1.4 MHz
 
There is a simple formula for use at radio frequencies, that uses realistic component values.

It is

L = 25330.3 / (F * F * C)

where L is in uH
C is in pF
F is in MHz

8.4 X10 -11 F is 84 pF
1400 KHz is 1.4 MHz
 

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