Figure 1 on the following page shows an LRC circuit with the resistor of 10 ?, t

Question

Figure 1 on the following page shows an LRC circuit with the resistor of 10 ?, the capacitor of 330 ?F, and the inductor of 8.2 mH.

(a) Calculate the resonance frequency in radian/s for the LRC circuit. (

b) If the angular frequency of the applied AC source is 628 radian/s, calculate

The impedance of the resistor =

The impedance of the capacitor =

The impedance of the inductor =

(c) If the current is measured as I(t) = 0.1× cos[(628 radian/s) t] (A), calculate

VR(t) =

VC(t) =

VL(t) =

Explanation / Answer

part A:

at resonance W^2 = 1/LC

W^2 = 1/(8.2 *10^-3 * 330*10^-6)

W = 608 rad/s

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part B :

when W = 628 rad/s

Impedence across Capacitor Xc = 1/wC = 1/(628 * 330 e -6)

Xc = 4.82 ohms

Impedence across inductor XL = wL = 628 * 8.2*10^-3 = 5.14 ohms

Impedence Z^2 = R^2 + (XL-Xc)^2

Z^2 = 10^2 + (5.14 - 4.82)^2

Z = 10.05 ohms

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part C:

V across R = = iR = 0.1 cos 628 * 10 = 0.949 Volts

V across C = i XC = 0.1 cos 628 * 5.14 = 0.488 Volts

V across L = iXlL = 0.1 cos 628 * 4.82 = 0.457 Volts

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