Suppose you are stranded on an island and need to make a radio

QUESTION

Need complete formula or expression for parts a, b and cSuppose you are stranded on an island and need to make a radio so that you can get weather updates. You know that weather updates for your general area can be found on short-wave radio within the frequency range flow to fhigh . Also, you manage to scavenge some thin, insulated wire of thickness d, of which you can allocate a length l to make a solenoid inductor. You also manage to find a long plastic tube of length a and diameter D, a large roll of foil of width w, a large mylar sheet of thickness 1100d and dielectric constant κ=3 that will accomodate the area of the foil, a speaker from headphones with impedance R, and a small transistor.Being extra resourceful, you manage to make a small battery out of a lemon, a galvanized nail, and a nickle that you attach to the transistor and headphone speaker to amplify the radio signal (FYI, this can also be done with a penny, some rain water, a piece of foil, and a paper towel).Part A – Assuming that you use the entire length l of wire for the inductor, as well as the plastic tube as a form, what is the maximum inductance achievable?The formula for the inductance of a solenoid is L=NΦi , where N is the number of turns, Φ is the megnetic field flux, and i is the instantaneous current provided by the battery and transister.Part B – Assuming that you intend to make a parallel plate capacitor out of the foil with capacitance that can be varied by the area of overlap of the two foil plates, what is the minimum length of foil needed to build the radio to capture the entire frequency range between flow and fhigh?At what frequency will the circuit resonate when only half the area of each capacitor plate overlaps?

ANSWER:

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