A general theory for the current in coupled antennas is formulated in terms of the vector potential and applied to determine the self-impedance Zs1 and the mutual impedance Z12 of a center-driven antenna in the presence of a second parallel, identical antenna which may be center-driven or center-loaded in an arbitrary way. Each antenna has a half-length h, a radius a, and the distance between them is b. Curves are shown for Zs1 and Z12 for h=λ/4; Ω=2 ln (2h/a) = ∞, 30, 20, 10; 0.05≦b/λ≦0.4; and for h=λ/2; Ω=2 ln (2h/a) = 30, 20, 10; 0.05≦b/λ≦0.5. It is shown that except for the special case of an indefinitely thin antenna (Ω= ∞) the self-impedance Zs1 of an antenna in the presence of a second antenna differs from the self-impedance Z0 when the antenna is isolated and varies with b/λ. The input impedance Zlin is determined and plotted for the same values of h and Ω, and the same ranges of b/λ for the following special cases: 1. The antennas are both center-driven in phase by identical generators. 2. The antennas are both center-driven in opposite phase by identical generators; or a driven antenna is parallel to a perfectly conducting plane. 3. Antenna 1 is center-driven; antenna 2 is parasitic and unloaded. 4. Antenna 1 is center-driven, antenna 2 is parasitic and center-tuned to self-resonance (h=λ/2 only).