# Role of antenna length

Consider a receiving dipole antennae of length $L$. If electromagnetic waves of power intensity $P$ W/m2 is incident on it, then open circuit voltage induced in the antenna is given by

$$V=\frac{L}{2}\sqrt{P\times 2\times 377}$$

where $V$ is independent of the wavelength of the electromagnetic waves.

Another fact is that dipole antennae are resonant at half wavelength.

How to reconcile these two facts? I mean to say a dipole of 6cm is resonant for 2.4GHz. But if one uses it for receiving 10 Mhz signal, what exactly will be problem as the open circuit voltage will be same irrespective of frequency (of course $P$ is constant)?

My understanding says following. While voltage induced will be same, what will depended on frequency is impedance of antenna. At half wavelength, the dipole will be resistive only. At lower frequencies capacitive reactance will be high while at high frequencies inductive reactance will be high, both these will reduce the current induced in the circuit.

Am I wrong? or, am I missing some aspect?

• the amateur radio stack exchange has lots of experts on it who can answer this question. they are nice guys too. Sep 4 '18 at 16:36