Final answer:
To produce a radio wave of a specific wavelength in an RLC circuit, such as the one described in the question, we can use the formulas for resonant frequency and wavelength.
By rearranging the equation for frequency, we can find the size of the inductor needed.
Step-by-step explanation:
In an RLC circuit, the resonant frequency is given by the formula f = 1 / (2π√(LC)), where f is the frequency, L is the inductance, and C is the capacitance.
In this case, the wavelength of the radio wave is given as 123 m.
The formula for calculating wavelength is λ = c / f, where λ is the wavelength, c is the speed of light (approximately 3x10^8 m/s), and f is the frequency.
To find the size of the inductor, we can rearrange the equation for frequency to solve for L:
L = 1 / (4π^2f^2C).
Plugging in the given values, we have
L = 1 / (4π^2(3x10^8 / 123)^2(4.67x10^-12)).
Plugging these values into a calculator, we find that the size of the inductor needed is approximately 2.41 µH.