Need help!!! For a series RLC circuit with resistance 5 KOhm, capacitance 100 pi

Question

Need help!!!

For a series RLC circuit with resistance 5 KOhm, capacitance 100 picoFarad, and inductance 0.025 Henry, what is the inductive and capacitive reactance, and the impedance at frequency 80 kHz, and what are the natural and the free oscillation mode frequencies? Provide the results within 1 Hz accuracy.

Experimentally, the free oscillation mode frequency is obtained by a read out from the oscilloscope screen. A student has found that 5 full periods of the damped oscillations cover 5.0 major divisions on the horizontal scale, with time-sweep knob indicating 10 microsecond/division. What is the frequency obtained from the experimental read out? With preserved setting of the oscilloscope (and a time-sweep subdivision being 0.2 of the horizontal division), is it possible to distinguish this read out from the resonance frequency f0 theoretically obtained in Problem 1, and examined experimentally too?

Explanation / Answer

inductive reactance(XL) = (WL) = *2*pi* 80KHz*0.025 H = 1.256*10^5

capacitive reactance (Xc) = 1/(WC) = 1/(2*pi * 80 KHz * 10^-10 F = 1.98 *10^4

Impedence = sqrt ( R^2 + (XL - XC)^ )

= sqrt( ( 5*10^3)^2 + ( 1.256*10^5 - 1.98*10^4)^2)

=1.05*10^5

The natural frequency is the frequency at which the system will oscillate unaected by outside forces. When we consider the oscillation of a pendulum, the gravitational force is considered to be an inherent part of the system.

free oscillation is an oscillating system in which all parts of the system move sinusoidally with the same frequency and with a fixed phase relation and their natural frequencies that depend on its structure, materials and boundary conditions.

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