1. consider a parallel RLC circuit with a current source, where: i(t)=10sqrt(2)cos(wt) mA, GR=3 mS, L=2/9 H, and C=1/2 microF. (a)At w = 1000 rad/s, what is the power factor of the load as seen by the current source? Is it leading or lagging? What kind and value of an element (resistor, inductor or capacitor) needs to be connected in parallel with the existing elements to produce unity power factor as seen by the source at this frequency? Insert the additional element in the circuit above.
(b) At unity power factor, the load is purely resistive, which defines resonance. Obtain the quality factor, the bandwidth and the lower and upper half-power frequencies with the added element.
(c) Return to the original circuit (without the additional element) for the remainder of this problem. At w=1000 rad/s, find the complex power absorbed by each element, the peak energies stored by the capacitor and the inductor, and the average power dissipated by the resistor.
(d) Obtain the angular frequency of resonance, the quality factor, the bandwidth and the lower and upper half-power frequencies of the original circuit.
(e) At the resonant frequency w0, find the complex power absorbed by each element, the peak energies stored by the capacitor and the inductor, and the average power dissipated by the resistor.
(f) Calculate the energy dissipated by the load in one cycle WD and verify that the quality factor matches the value obtained in part d) using the energy definition of the quality factor.