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//Problem 28.08: An R–L–C series circuit has a resonant frequency of 1.2 kHz and a Q-factor at resonance of 30. If the impedance of the circuit at resonance is 50 ohm determine the values of (a) the inductance, and (b) the capacitance. Find also (c) the bandwidth, (d) the lower and upper half-power frequencies and (e) the value of the circuit impedance at the half-power frequencies.
//initializing the variables:
Zr = 50; // in ohms
fr = 1200; // in Hz
Qr = 30; // Q-factor
//calculation:
//At resonance the circuit impedance, Z
R = Zr
wr = 2*%pi*fr
//Q-factor at resonance is given by Qr = wr*L/R, then L is
L = Qr*R/wr
//At resonance r*L = 1/(wr*C)
//capacitance, C
C = 1/(L*wr*wr)
//bandwidth,.(f2 − f1)
bw = fr/Qr
//upper half-power frequency, f2
f2 = (bw + ((bw^2) + 4*(fr^2))^0.5)/2
//lower half-power frequency, f1
f1 = f2 - bw
//At the half-power frequencies, current I
//I = 0.707*Ir
//Hence impedance
Z = (2^0.5)*R
printf("\n\n Result \n\n")
printf("\n (a)inductance, L is %.3f H ",L)
printf("\n (b)capacitance, C is %.2E F ",C)
printf("\n (c)bandwidth is %.0f Hz ",bw)
printf("\n (d)the upper half-power frequency, f2 is %.0f Hz and the lower half-power frequency, f1 is %.0f Hz ",f2,f1)
printf("\n (e)impedance at the half-power frequencies is %.2f ohm ",Z)
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