Question

How the effective power radiated by an antenna will be changed if the wavelength of radiation is decreased?

Answer 1

Hint: The effective power radiated by an antenna directly depends on the frequency of the electromagnetic radiation. And, the frequency is inversely proportional to the wavelength of radiation.
Therefore, the effective power is inversely proportional to the wavelength of radiation.

Formula Used: The effective power radiated by an antenna is related to the wavelength of radiation as follows: \[P \propto \dfrac{1}{{{\lambda ^2}}}\]

Complete step by step solution:
Antenna is an instrument required for radiating and receiving
Electromagnetic waves. The effective power radiated by an antenna varies inversely as the square of length of the antenna. Thus,
\[P \propto \dfrac{1}{{{l^2}}}\]\[ \to (1)\]
where, \[P\] is the effective power radiated by an antenna and \[l\] is the length of the antenna.
The required antenna length depends upon the wavelength of the radiation such that shorter the wavelength, shorter is the antenna. So, equation (2) can also be written as
\[P \propto \dfrac{1}{{{\lambda ^2}}}\]\[ \to (2)\]
where, \[\lambda \] is the wavelength of radiation.
From equation (2), the effective power radiated by an antenna varies inversely with the square of the wavelength of radiation. Therefore if the wavelength of radiation is decreased, the effective power radiated by an antenna will increase.

Note: The power radiated by an antenna does not only depend on the length of the antenna, but also the connection to the radio or transmitter and the distance of the receiving antenna from the transmitting antenna. The total received power is calculated and summed up over all possible angles of the reception of waves.