Parallel RLC Circuit: Find Current I & Resonance Condition

[libelec]

Homework Statement

For the following circuit:

where R1 = 100k$$\Omega$$, R2 = 10$$\Omega$$, L = 0,1Hy, C = 200$$\mu$$F. V gives a constant tension of 1V. Find the current I as function of the frecuence, the condition of resonance, and the condition R1 and R2 must have so that the Q factor = 0,5

Homework Equations

The Attempt at a Solution

The problem is that I can't define de phase phi due to the lack of information about the frecuence, plus the expressions for the current I that I found are ugly.

I condensed the resistance R1 and the inductance L into the impedance Z1 = R1 + jwL, and the resistance R2 and the capacitance C into the impedance Z2 = (1/R1 - jwC)^-1. Then I condensed those two into the impedance Z3 = Z1 + Z2.

I find this process very annoying, especially considering that I have to find the inverse of a complex number.

What faster way can I use to solve the problem? Because if I use Kirchoff's First and Second Rule I get an uglier equation system.

 

[libelec]

Anybody?