Filtering Signals

You have been tasked with creating a signal filter using only an inductor ($L$) and a resistor ($R$). By connecting the two elements in series with a sinusoidal driver ($V(t) = V_0 \sin(\omega t)$), show you can create both a low-pass and high-pass filter using just connecting the output signal across the different circuit elements.

Use the method of phasors to simplify your approach (i.e., finding the ratio of the input voltage and output voltage). Check that you answers make sense in the limit of low and high frequency signals.