The LC circuit of a radar transmitter oscillates at 22.00 GHZ. (a) What inductan

Question

The LC circuit of a radar transmitter oscillates at 22.00 GHZ. (a) What inductance will resonate with a 1.00 pF capacitor at this frequency? (b) What is the inductive reactance of the circuit at this frequency? An LC generator with an output rms voltage of 24 V at a frequency of 50 Hz is connected across a 4 mu F capacitor. Find the following. (a) capacitive reactance. ohm (b) rms current A (c) maximum current in the circuit A (d) Does the capacitor have its maximum charge when the current takes its maximum value?

Explanation / Answer

part a:

oscillation frequency=1/(2*pi*sqrt(L*C))

where L=inductance

C=capacitance

given C=1 pF=10^(-12) F

frequency=22*10^9 Hz

then 22*10^9=1/(2*pi*sqrt(L*10^(-12))

==> sqrt(L*10^(-12))=1/(2*pi*22*10^9)

==>L=1/(10^(-12)*(2*pi*22*10^9)^2)=5.2335*10^(-11) H

part b:

inductive reactance=2*pi*22*10^9*L

=2*pi*22*10^9*5.2335*10^(-11)

=7.2343 ohms

Q9.

part a:

capacitive reactance=1/(2*pi*frequency*C)

=1/(2*pi*50*4*10^(-6))

=795.77 ohms

part b:

rms current=rms voltage/capacitance reactance

=24/795.77=0.03016 A

part c:

maximum current=sqrt(2)*rms current

=0.042652 A

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