The circuit below represents an AC circuit in steady-state in the phasor domain (for the complex numbers, you may assume units are V, A, $\Omega$, etc. as appropriate). Both sources in the circuit have the same $\omega$, but you are not told the value of $\omega$. Each box represents the impedance of a single circuit element (a resistor, capacitor or inductor).
a. What are the maximum values of waveforms $v_s(t)$ and $i_s(t)$? Enter your answers as $Y_1$ and $Y_2$, with $Y_1 = \frac{V_{s_{max}}}{\sqrt{2}}$ and $Y_2 = i_{s_{max}}$.
b. We now double $\omega$ of both sources but keep everything else the same (such as the capacitor, inductor and resistor values; the amplitude and phase of the sources, etc.). Find the new value of all complex numbers in the circuit (the new value of $a_1$ is called $a_2$, etc.) as well as the new magnitude of the current source $|I_s| = X_2$.
$V_s = d_1 + e_1j$
Given Variables:
$a_1$: 50
$b_1$: -18
$c_1$: 9
$d_1$: 2
$e_1$: 2
$X_1$: 4 A
Calculate the following:
