please show work and give detailed explanation. Thank you! Figure 1 on the follo

Question

please show work and give detailed explanation. Thank you!

Figure 1 on the following page shows an LRC circuit with the resistor of 10 Ohm, the capacitor of 330 mu 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 times cos[(628 radian/s> t] (A), calculate V_R (t) = V_C (t) = V_L (t) =

Explanation / Answer

2)

a) resonance frequency = 1/sqrt(L * C)

resonance frequency = 1/sqrt(330 *10^-6 * 0.0082)

resonance frequency = 607.9 rad/s

b)

impedance of resistor = 10 Ohm

impedance of capacitor = -j/(w * C)

impedance of capacitor = -j/(628 * 330 *10^-6)

impedance of capacitor = -4.82 j Ohm

impedance of inductor = j * w * L

impedance of inductor = j * 628 * 0.0082

impedance of inductor = 5.15 j

c)

for the voltages

V(R) = 0.10 * 10 * cos(628 * t)

V(R) = 1 * cos(628 * t)

V(C) = 4.82 * 0.1 * cos(628 * t - pi/2)

V(C) = 0.482 * cos(628 * t - pi/2)

V(L) = 5.15 * cos(628 * t + pi/2) * 0.10

V(L) = 0.515 * cos(628 * t + pi/2)

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