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+//Problem 28.04: A series circuit comprises a 10 ohm resistance, a 5 μF capacitor and a variable inductance L. The supply voltage is 20/_0° volts at a frequency of 318.3 Hz. The inductance is adjusted until the p.d. across the 10 ohm resistance is a maximum. Determine for this condition (a) the value of inductance L, (b) the p.d. across each component and (c) the Q-factor.

+

+//initializing the variables:

+R = 10; // in ohms

+C = 5e-6; // IN fARADS

+rv = 20; //in volts

+thetav = 0; // in degrees

+f = 318.3; // in Hz

+

+//calculation:

+wr = 2*%pi*f

+//The maximum voltage across the resistance occurs at resonance when the current is a maximum. At resonance,L = 1/c*wr^2

+L = 1/(C*wr^2)

+//voltage

+V = rv*cos(thetav*%pi/180) + %i*rv*sin(thetav*%pi/180)

+//Current at resonance Ir

+Ir = V/R

+//p.d. across resistance, VR

+VR = Ir*R

+//inductive reactance, XL

+XL = wr*L

+//p.d. across inductance, VL

+VL = Ir*(%i*XL)

+//capacitive reactance, Xc

+Xc = 1/(wr*C)

+//p.d. across capacitor, Vc

+Vc = Ir*(-1*%i*Xc)

+//Q-factor at resonance, Qr

+Qr = imag(VL)/V

+

+printf("\n\n Result \n\n")

+printf("\n (a)inductance, L is %.2E H ",L)

+printf("\n (b)p.d. across resistance, VR is %.2f V, p.d. across inductance, VL %.0fi V and p.d. across capacitor, VC %.0fi V ",VR, imag(VL), imag(Vc))

+printf("\n (c)Q-factor at resonance, Qr is %.0f  ",Qr)
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