Short analysis of AC circuit
There are only two ways that the current through a resistor can be independent of the value of the resistor:


The current is zero. This means that the applied voltage must be zero as well. Your solution of making the capacitance infinite (effectively a short circuit) falls into this category.
The resistor is connected to a current source. Here's a hint: The circuit as given shows a voltage source connected in series with an inductor, a Th&eacute;venin source. It can be redrawn as its Norton equivalent: a current source in parallel with that same inductor. This effectively puts the inductor in parallel with the capacitor and the resistor, too. Is there a way to make sure that all the current from the current source flows through only the resistor?