Question

If a transmitting antenna of a height of 105m is placed on a hill, then what is its coverage area?
A. \[{\rm{4224 k}}{{\rm{m}}^{\rm{2}}}\]
B. \[{\rm{3264 k}}{{\rm{m}}^{\rm{2}}}\]
C. \[{\rm{6400 k}}{{\rm{m}}^{\rm{2}}}\]
D. \[{\rm{4864 k}}{{\rm{m}}^{\rm{2}}}\]

Answer 1

Hint:Before we proceed with the problem let’s see what is given. We need to find the coverage area of an antenna; they have given the height of the antenna from the hill station. By finding the maximum distance covered by the signal from the antenna we can easily calculate the coverage area by the antenna.

Formula Used:
The formula to find the coverage area is given by,
\[A = \pi {d^2}\]……… (1)
Where, d is the range of the antenna.

Complete step by step solution:
In order to find the coverage area first, we need to find the range of the antenna. The range of the antenna (maximum distance covered) is given by,
\[d = \sqrt {2Rh} \]
Here, R is the radius of the earth and h is the height of the antenna.
Substitute value of d in equation (1) we obtain,
\[A = \pi {\left( {\sqrt {2Rh} } \right)^2}\]
\[ \Rightarrow A = \pi \times 2Rh\]
Here, \[h = 105m\], We know that, \[R = 6400km\]
\[ \Rightarrow A = 3.142 \times 2 \times 6400 \times 105\]
\[ \Rightarrow A = 4222.8k{m^2}\]
\[ \therefore A \simeq 4224{m^2}\]
Therefore, the coverage area of the antenna is \[4224{m^2}\].

Hence, option A is the correct answer.

Note: An antenna is basically a bunch of conductors (metallic in nature) arranged in some specific shape that is connected to either a transmitter or receiver to send or receive RF signals. In general, they are multi-directional in nature, i.e., they are able to operate in all directions. They can be designed such that they become omni-direction when required. If the distance the signal needs to be transmitted across is large then it might have to be electrically powered to generate this huge transmission range.