# What is the difference between antenna input impedance and its radiation resistance?

I got to know that the input impedance of the halfwave dipole antenna is given as:

$$Z_{in}$$=1/$$I_m$$* sin($$\beta$$(H-|Z|))

where $$I_m$$ is the maximum current on the antenna( when excited with a 1 volt supply),

H is the half-length of the antenna,

Z is the position on the antenna and $$\beta$$ is wave number.

Apart from the input impedance there is another parameter called as radiation resistance calculated by dividing the $$I_m^2$$ from the power radiated by the antenna.

Now my doubts are:

1. Are both the radiation resistance and the input impedance one and the same?
2. If I take a full wave dipole ($$\beta*H$$=$$\pi$$) then at Z=0 ( input terminal) the input impedance value becomes infinite which is similar to open circuit condition so does that mean there wouldn't be any radiation by the antenna?
3. If I consider the current distribution of the antenna for the full wave dipole (as given in the figure, the current standing wave value becomes zero at the input end of the antenna how can there be a distribution of the current on the antenna if the input current is zero? I seem to have confused myself a lot. kindly clarify me on this doubt.Thank you in advance.