Find the resonant frequency of a circuit that has a 400 mH inductor and a 30 nF capacitor connected in series.
A) Canadian FM radio station (CLAW) broadcasts lobster information at 95.9 MHz. find the wavelength of this station.
B) What would be the frequency of a station for which the carrier wave was 400 m long?
if the average speed of light in a medium is 2.2x10E8 m/s, what is the medium’s index of refraction?
Find the resonant frequency of a circuit that has a 400 mH inductor and a 30 nF capacitor connected in series.
f= .159/sqrt(LC)
A) Canadian FM radio station (CLAW) broadcasts lobster information at 95.9 MHz. find the wavelength of this station. freq*wavelength=speedlight
B) What would be the frequency of a station for which the carrier wave was 400 m long? same formula
if the average speed of light in a medium is 2.2x10E8 m/s, what is the medium’s index of refraction?
index=speelightinfreespace/speedinMedium
To find the resonant frequency of a series circuit with an inductor and a capacitor, you can use the formula:
f = 1 / (2π√(LC))
where f is the resonant frequency, L is the inductance, and C is the capacitance.
For the given circuit with a 400 mH (millihenries) inductor and a 30 nF (nanofarads) capacitor, you need to convert the units to henries (H) and farads (F) respectively, using the following conversions:
1 mH = 0.001 H
1 nF = 0.000000001 F
Substituting the converted values into the formula:
L = 400 mH = 0.4 H
C = 30 nF = 0.00000003 F
f = 1 / (2π√(0.4 * 0.00000003))
Simplifying the equation:
f = 1 / (2π√(0.000012))
f = 1 / (2π * 0.003464)
f ≈ 1 / 0.02182
f ≈ 45.85 Hz
So, the resonant frequency of the circuit is approximately 45.85 Hz.
Now, let's move on to the other questions:
A) To find the wavelength of a radio station's frequency, you can use the formula:
λ = c / f
where λ is the wavelength, c is the speed of light, and f is the frequency.
Given that the radio station broadcasts at 95.9 MHz, convert this frequency to hertz:
95.9 MHz = 95.9 × 10^6 Hz
Substituting the values into the formula:
λ = 2.2 × 10^8 m/s / (95.9 × 10^6 Hz)
Simplifying the equation:
λ = 2.29 meters (rounded to two decimal places)
Therefore, the wavelength of the Canadian FM radio station (CLAW) broadcasting at 95.9 MHz is approximately 2.29 meters.
B) To find the frequency for a station with a carrier wave length of 400 m, you can rearrange the formula for wavelength:
f = c / λ
Substituting the given values into the formula:
f = 2.2 × 10^8 m/s / 400 m
Simplifying the equation:
f = 550,000 Hz (rounded to two decimal places)
Therefore, the frequency of a station with a carrier wave length of 400 m would be approximately 550,000 Hz.
Moving on to the last question:
To find the medium's index of refraction, you can use the formula:
n = c / v
where n is the index of refraction, c is the speed of light in a vacuum, and v is the average speed of light in the medium.
Given that the average speed of light in the medium is 2.2 × 10^8 m/s, and the speed of light in a vacuum is approximately 3 × 10^8 m/s, substitute the values into the formula:
n = (3 × 10^8 m/s) / (2.2 × 10^8 m/s)
Simplifying the equation:
n ≈ 1.36
Therefore, the medium's index of refraction is approximately 1.36.