If given a device that has unknown circuitry, and you measure that the voltage across the device leads the voltage across a resistor at 500 Hz, can you know what type of elements are in the device? If so, how?

Inductor.

Explanation:

it is given that, the voltage across the device leads the voltage across a resistor at 500 Hz. The device that has unknown circuitry can be a inductor. For LC circuit, the voltage across the inductor leads the voltage across resistor. So, the device can be a inductor.