An LRC circuit has an inductance of 1.16 x 10^-8 H, a capacitance of 2.13x10 ^-1

Question

An LRC circuit has an inductance of 1.16 x 10^-8 H, a capacitance of 2.13x10 ^-12 F, and a dc resistance of 4.52 Ohms. It is driven at a frequency of 924 MHz by a sinusoidal ac source with a peak voltage of 375V. A) Find the capacitive reactance, the inductive reactance and total reactance of the circuit. Is this circuit primarily capacitive or inductive? B) Using the above values, find the impedance and phase angle of the circuit. C) Find the peak current through the circuit. D) Find the peak voltages across the resistor, inductor and capacitor.

Explanation / Answer

a)

capacitive reactance Xc = 1/wc = 1/(2*pi*924*2.13*10^-12) = 8.1*10^7 ohms

inductive reactance XL = wL = 2*pi*924*1.16*10^-8 = 6.734*10^-5 ohms

reactance = Xc-XL

Z = (8.1*10^7-6.734*10^-5) = (8.1*10^7

(b)

z = sqrt(R^2+(Xc-XL)^2)

z = 8.1*10^7 ohms

tanphi = (Xc-XL)/R

tanphi = 90

(c)

Imax = Emax/z = 4.63 uA

(d)

VR = Imax*R = 4.63*10^-6*4.52 = 2.1*10^-5 V

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