Final answer:
The capacitance of a parallel plate transmission line with an air dielectric decreases as the distance between the plates increases while increasing the plate area and introducing dielectric results in increased capacitance.
Step-by-step explanation:
In a parallel plate transmission line with an air dielectric, the capacitance of the transmission line will decrease as the distance between the plates increases. This is because capacitance is inversely proportional to the distance between the plates (C = ε0A/d where ε0 is the permittivity of free space, A is the area of the plates, and d is the distance between them). Therefore, if you double the distance between capacitor plates, the capacitance will decrease by half (Option b). Conversely, when the area of the plates increases, while the voltage remains constant, both the capacitance and the stored energy increase (Option d).
Furthermore, if you introduce a dielectric material between the plates, the capacitance increases due to the reduction in the electric field strength, which results in a smaller voltage (V = Ed) for the same charge, elevating the capacitance since C = Q/V. For example, doubling the area of a capacitor and reducing the distance by four will increase the capacitance eightfold (Option d).