Trapped on a deserted island, you salvage some copper wire and a generator to bu

Question

Trapped on a deserted island, you salvage some copper wire and a generator to build a makeshift radio transmitter.

a) If you wrap the wire into an 8-turn coil of radius 3.8 cm and length 25cm, what is its inductance?

b) What capacitance do you need to make an RLC circuit with the coil that oscillates at the emergency beacon frequency of 406 MHz?

c) If you fashion the parallel-plate capacitor out of two aluminum squares, 5.0 cm on a side, what should be the separation distance between the two plates?

Explanation / Answer

Here ,

a)

inductance = N^2 * u0 * A/L

inductance = 8^2 * 4pi *10^-7 * 0.038^2/.25

inductance = 4.64 *10^-7 H

b)

let the capcitance is C

f = 1/(2pi * sqrt(L * C))

406 *10^3 = 1/(2pi * sqrt(4.64 *10^-7 * C))

solving for C

C = 3.31 *10^-7 F

c)

let the seperation needed is d

3.31 *10^-7 = 8.854 *10^-12 * 0.05^2/d

solving for d

d = 6.68 *10^-8 m

the seperation of the the plates must be 6.68 *10^-8 m

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