3. In the circuit below, the voltage source phasor is $V = V_0 exp(i\omega t)$ and the current phasor through the source is $I = I_0 exp(i(\omega t - \phi))$. (a) Find the complex admittance $1/Z = Re(1/Z) + i Im(1/Z)$ of the circuit. Write down explicitly $Re(1/Z)$ and $Im(1/Z)$. (b) Using Ohm's law for phasors, $I = 1/Z \, V$, find the current phasor $I = I_0 exp(i(\omega t - \phi))$ through the battery, that is, find the amplitude $I_0$ and the phase shift $\phi$. (c) Using Kirchhoff's loop rules, find the current phasors $I_1$ through C and the current phasor $I_2$ through R and L, expressed in terms of V. (d) What is the resonance condition, in terms of R, C, and L?
