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

In summary, the question is what must be the value of the inductance in order for an AM station broadcasting at 1400 kHz with a capacitance of 8.4X10-11 F to be tuned in. The formula for the natural frequency of an LC circuit is w=(L*C)^(1/2), and plugging in the values of f=1400 Khz and w=2*pi*f, we get L=1.5385*10^-10 Henries. However, there is a simpler formula for radio frequencies that uses realistic component values, which is L = 25330.3 / (F * F * C). Using this formula and converting the given values to the appropriate units,
  • #1
jandominic145
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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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  • #2
What is the natural frequency of an LC circuit oscillation?
 
  • #3
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
 
  • #4
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
 
  • #5
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
 

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

What is the meaning of "AM" in "AM station"?

"AM" stands for amplitude modulation, which is a method of transmitting radio waves by varying the amplitude (strength) of the wave. This is different from FM (frequency modulation), where the frequency of the wave is varied.

What does 1400 kHz mean in relation to the radio wave?

1400 kHz (kilohertz) is the frequency of the radio wave being broadcasted by the AM station. It represents the number of waves (cycles) that pass through a point in one second. A higher frequency means more waves passing through in a given time, resulting in a higher pitch or more energy.

How far can an AM station's radio wave travel?

The range of an AM station's radio wave depends on several factors such as the power of the transmitter, the height of the antenna, and the terrain of the area. Generally, AM waves can travel up to a few hundred miles during the day and even further at night due to atmospheric changes. However, buildings and other obstructions can also affect the range of the wave.

How is the quality of an AM station's broadcast determined?

The quality of an AM station's broadcast is determined by the strength and clarity of the radio wave received by the listener's radio. Factors such as distance, interference from other stations, and atmospheric conditions can affect the quality of the broadcast.

Can a radio wave with a frequency of 1400 kHz be harmful to humans?

No, AM radio waves are not harmful to humans. They fall under the category of non-ionizing radiation, which means they do not have enough energy to ionize atoms and cause harm to living organisms. AM radio waves have been used for decades without any evidence of negative health effects on humans.

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