A radar transmitter contains an LC circuit oscillating at 2.10 × 1010 Hz. (a) Fo

Question

A radar transmitter contains an LC circuit oscillating at 2.10 × 1010 Hz. (a) For a one-turn loop having an inductance of 360 pH to resonate at this frequency, what capacitance is required in series with the loop? 0.00159X Your response is off by a multiple of ten. p (b) The capacitor has square, parallel plates separated by 1.60 mm of air. What should the edge length of the plates be? 1.69 Your response differs from the correct answer by more than 10%. Double check your calculations. mm c) What is the common reactance of the loop and capacitor at resonance? 47.5 Need Help?ReadIN

Explanation / Answer

here,

frequency , f = 2.1 * 10^10 Hz

a)

indiuctance , L = 360 pH = 3.6 * 10^-10 H

let the capacitance be C

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

2 * pi * 2.1 * 10^10 = 1/sqrt(3.6 * 10^-10 * C)

solving for C

C = 1.6 * 10^-13 F = 0.16 pF

the capacitance is 0.16 pF

b)

let the edge length be a

d = 1.6 mm = 0.0016 m

capacitance , c = area * e0 /d

1.6 * 10^-13 = a^2 * 8.85 * 10^-12 /(0.0016)

solving for a

a = 5.34 * 10^-3 m = 5.34 mm

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