Question

A signal is to be transmitted through a wave of wavelength $\lambda$, using a linear antenna. The length $l$ of the antenna and effective power radiated $P_{eff}$ will be given respectively as :
(K is a constant of proportionality)

• A. $\frac{\lambda }{16},P_{eff}=K{\left(\frac{1}{\lambda }\right)}^3$
• B. $\lambda ,P_{eff}=K{\left(\frac{1}{\lambda }\right)}^2$
• C. $\frac{\lambda }{8},P_{eff}=K\left(\frac{1}{\lambda }\right)$
• D. $\frac{\lambda }{5},P_{eff}=K{\left(\frac{1}{\lambda }\right)}^{\frac{1}{2}}$

Answer 1

Answer: (B)

$\lambda ,P_{eff}=K{\left(\frac{1}{\lambda }\right)}^2$

Power radiated by antenna, $P_r\propto {\left(\frac{L}{\lambda }\right)}^2$

${\Rightarrow P}_r\propto \left(\frac{1}{{\lambda }^2}\right)$

${\Rightarrow P}_r=K{\left(\frac{1}{\lambda }\right)}^2$

$\Rightarrow$Length of Antenna, $L\propto \lambda$

(Usually $L=\frac{\lambda }{4}$, where power peaks)

Therefore, option 2.