Q. I was able to calculate Vrms across the inductor, resistor, and capacitor separately (parts a, b and c), but I was having trouble calculating Vrms across the inductor and resistor in series and the resistor and capacitor in series (parts C and D).
I think part of my problem is I don't know how to incorporate the fact that Irms is in different phases in each...
How would one do this?
A. If you calculate the rms current through the circuit, then the rms voltage across any element, or set of elements, is simply Vrms=IrmsZ, where Z is the total impedance of the element(s) (see Eq. 29-51). You can get the rms current by evaluating Irms=Erms/Z, where Erms is the alternating source emf. If you do this, then you don't have to worry about all of the phases explicitly.
If you do want to worry about phases, then you have to figure out the phase of the voltage across each element and then sum the voltages across the various elements. This can be quite an exercise in trigonometry! It's much easier to use Ohm's law, as generalized for AC circuits.