Question

A $TV$ transmitting antenna is $81\, m$ tall. It has a half-power beam width of 10 degrees. If the receiving antenna is at the ground level, the service area covered by the transmitter is determined by

• A. The Half-power beam width, the height of the transmitter and the radius of the earth
• B. The height of the transmitter and the radius of the earth
• C. The half-power beam width and the radius of the earth
• D. The height of the transmitter and the half-power beam width
• E. The height of the transmitter

Answer 1

Answer: (B)

The relation of the distance covered by a transmitting antenna is given by
$D=\sqrt{2 h R}$
where, $h=$ height of antenna
and $R=$ radius of earth.
Since, the area covered is circular in shape which has antenna located at centre.
$\therefore $ Total surface area covered by the transmitter Area $=\pi D^{2}=2 \pi h R$
So, the service area covered by antenna is depend on the height of antenna and radius of earth.