• # question_answer In communication system the range is R, if the height of antenna is doubled, then what will be the increase in range?

41.4% Transmission range $d=\sqrt{2hR}$ where, h is the height of antenna and R is the radius of earth. $\therefore$      $d\propto \sqrt{h}$ If the height of antenna is doubled, $d'\propto \sqrt{2h}$ $\frac{d'}{d}=\frac{\sqrt{2h}}{\sqrt{h}}=\sqrt{2}=1414$ $d'=1.414\,d=d\,(1+0.414)=d+0.414\,d$           $=d+\frac{41.4}{100}d=d+41.4%\,d$ i.e. the range is increased by 41.4%.