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Communication System

Section: Physics

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Question : 7 of 13

Marks: +1, -0

If the sum of heights of transmitting and receiving antennas in line of sight of communication is '

h

', then the height of receiving antenna, to have the range maximum is

[AP EAPCET 21 May 2025 S1]

$\;\frac{h}{2}$
$\;\frac{h}{4}$
$2 h$
$\;\frac{2h}{3}$

Solution:

The range of line of sight communication between two antennas is given by

x = \sqrt{2 R h_T} + \sqrt{2 R h_R}

Here,

h_T + h_R + h

Let

\;\; h_T = H

, then

\;h_R\;=h-H

\; \therefore x\; = \sqrt{2R} \left[ \sqrt{H} + \sqrt{h-H} \right]

\;\; \frac{dx}{dH} = \sqrt{2R} \; \left[ \frac{1}{2\sqrt{H}} + \frac{1}{2\sqrt{h-H}}(-1) \right] = 0

\Rightarrow \;\; \frac{1}{2\sqrt{H}} \;=\; \frac{1}{2\sqrt{h-H}}

H\;=h-H\;

\Rightarrow\;H\;=\;\frac{h}{2}

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