Given information:
- A 2-terminal network consists of one of the RLC elements.
- The element is connected to an AC supply.
- The current through the element is IA when an inductor is inserted in series between the source and element.
- The current through the element becomes 2IA when an inductor is removed and a capacitor is inserted in series between the source and element.

To determine the RLC element, let's analyze the behavior of each type of element when connected to an AC supply:

1. Resistor: A resistor opposes the flow of current and dissipates energy in the form of heat. In an AC circuit, the current and voltage are in phase, which means that the voltage across the resistor is proportional to the current flowing through it. Therefore, inserting an inductor in series with a resistor would increase the impedance of the circuit, reducing the current through the resistor. Similarly, inserting a capacitor in series with a resistor would decrease the impedance of the circuit, increasing the current through the resistor. However, in both cases, the change in current would be proportional to the change in impedance, which means that the current through the resistor would not change by a factor of 2.

2. Inductor: An inductor stores energy in a magnetic field and opposes changes in current. In an AC circuit, the voltage across an inductor lags behind the current by 90 degrees, which means that the impedance of the inductor is proportional to the frequency of the AC supply. Therefore, inserting an inductor in series with another inductor would increase the impedance of the circuit, reducing the current through both inductors by the same factor. Similarly, inserting a capacitor in series with an inductor would decrease the impedance of the circuit, increasing the current through both inductors by the same factor. However, in both cases, the change in current would be proportional to the change in impedance, which means that the current through the original RLC element would not change by a factor of 2.

3. Capacitor: A capacitor stores energy in an electric field and opposes changes in voltage. In an AC circuit, the current through a capacitor lags behind the voltage by 90 degrees, which means that the impedance of the capacitor is inversely proportional to the frequency of the AC supply. Therefore, inserting an inductor in series with a capacitor would decrease the impedance of the circuit, increasing the current through the capacitor by a factor of 2. Similarly, inserting a capacitor in series with a capacitor would increase the impedance of the circuit, reducing the current through the capacitor by a factor of 2. In both cases, the change in current is proportional to the change in impedance, which means that the current through the original RLC element would change by a factor of 2 only if it is a capacitor.

Therefore, the RLC element in the given circuit is a capacitor, and the correct answer is option 'C'.