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(A) For efficient transmission and reception of signals,the length $l$ of a linear antenna should be comparable to the wavelength $\lambda$ of the sig

Vedclass · Accepted Answer

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

Vedclass · Answer

(A) For efficient transmission and reception of signals,the length $l$ of a linear antenna should be comparable to the wavelength $\lambda$ of the signal. Typically,$l = \frac{\lambda}{4}$ or $l = \frac{\lambda}{2}$ are standard lengths. Among the given options,the length must be a fraction of $\lambda$.The power radiated $P_{eff}$ by a linear antenna is proportional to the square of the ratio of the antenna length to the wavelength. Specifically,$P_{eff} \propto \left(\frac{l}{\lambda}\right)^2$. Since $l$ is proportional to $\lambda$,we have $P_{eff} \propto \left(\frac{\lambda}{\lambda}\right)^2$ is not the case here; rather,for a fixed antenna length,the power radiated is inversely proportional to the square of the wavelength,i.e.,$P_{eff} \propto \frac{1}{\lambda^2}$.Thus,$P_{eff} = K \left(\frac{1}{\lambda}\right)^2$. Comparing this with the options,option $A$ provides the correct relationship for power,and the length $\lambda$ is a standard order of magnitude for antenna design.

List-$I$ (Layer of atmosphere)	List-$II$ (Approximate height over earth's surface)
$(A)$ $F_1$-Layer	$(I)$ $10\,km$
$(B)$ $D$-Layer	$(II)$ $170-190\,km$
$(C)$ Troposphere	$(III)$ $100\,km$
$(D)$ $E$-Layer	$(IV)$ $65-75\,km$

$A$ 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)

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