Question

For VHF signal broadcasting, ________ \[k{m^2}\]of the maximum service area will be covered by an antenna tower of height 30 m, if the receiving antenna is placed on the ground. Let the radius of the earth be 6400 km. (Take \[\pi \] as 3.14)

Answer 1

Hint:We need to understand the maximum effective area of a receiving antenna, by which we can determine many terms like how much power an antenna is receiving. The maximum distance between transmitting antenna and receiving antenna at which they can see each other is the maximum line of sight distance.

Formula used:
The maximum service area covered by an antenna is given as:
A=\[\pi {r^2}\]
Where r is the maximum line of sight distance and given as:
\[r = \sqrt {2hR} \]
Where h is the height and R is the radius of the earth.

Complete step by step solution:
Height of tower, h=\[30{\rm{ m = 30}} \times {\rm{1}}{{\rm{0}}^{ - 3}}{\rm{ km}}\]
Radius of the earth, R=6400 km
\[\pi = 3.14\]
As we know that area covered by the signal, A=\[\pi {r^2}\]
Here r is the maximum line of sight distance.
As we know \[r = \sqrt {2hR} \]

Now putting this value in above, we get the maximum service area covered by an antenna as,
\[A=\pi {(\sqrt {2Rh} )^2}\]
\[\Rightarrow A=\pi \times 2Rh\]
Substituting all the values, we get
\[A= 2 \times 3.14 \times 6400 \times 30 \times {10^{ - 3}}\\
\therefore A = 1205.76 \approx 1206\,{\rm{ k}}{{\rm{m}}^2}\]

Therefore, For Very high frequency (VHF) signal broadcasting, \[1206\,{\rm{ }}k{m^2}\] of the maximum service area will be covered by an antenna tower.

Note:Every antenna has an effective aperture. In a wire antenna, it doesn’t have width, so its area will become zero. Here the physical area may be zero or may be very small due to its width but to be an antenna it should have a high effective area. This effective area is an electrical concept.