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

Answer

Correct option: A.
$\lambda ,{P_{eff}} = K{\left( {\frac{1}{\lambda }} \right)^2}$
a
Length of antenna = comparable to $\lambda $

Power radiated by linear antenna inversely depends on the square of wavelength and directly on the length of the antenna. Hence

Power $P = \mu {\left( {\frac{1}{\lambda }} \right)^2}$  here $\mu \, = K$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Similar questions

A charged particle $q$ is placed at the centre $O$ of cube of length $L$ $(A\,B\,C\,D\,E\,F\,G\,H)$. Another same charge $q$ is placed at a distance $L$ from $O$.Then the electric flux through $BGFC$ is
To generate a power of $3.2\, mega\, watt$, the number of fissions of ${U^{235}}$ per minute is

(Energy released per fission $= 200\,MeV,  1\,eV = 1.6 \times {10^{ - 19}}J)$

Read the following statements:

$A.$ When small temperature difference between a liquid and its surrounding is doubled the rate of loss of heat of the liquid becomes twice.

$B.$ Two bodies $P$ and $Q$ having equal surface areas are maintained at temperature $10^{\circ}\,C$ and $20^{\circ}\,C$. The thermal radiation emitted in a given time by $P$ and $Q$ are in the ratio $1: 1.15$

$C.$ A carnot Engine working between $100\,K$ and $400\,K$ has an efficiency of $75 \%$

$D.$ When small temperature difference between a liquid and its surrounding is quadrupled, the rate of loss of heat of the liquid becomes twice.

Choose the correct answer from the options given below :

Three rods of equal length and cross sectional area and coefficient of thermal conductivities $K, 2K$ and $3K$ are joined as shown in figure temperature of their ends are $110\ ^oC, 20\ ^oC$ and $0\ ^oC$ respectively then temperature of junction will be ......... $^oC$
An electric heater of resistance $6 \,ohm$ is run for $10$ minutes on a $120\, volt$ line. The energy liberated in this period of time is
What will be the wave velocity, if the radar gives $54$ waves per min and wavelength of the given wave is $10\, m$  ......  $m/sec$
A particle moving in a straight line covers half the distance with speed $6 m / s$. The other half is covered in two equal time intervals with speeds $9 m / s$ and $15 m / s$ respectively. The average speed of the particle during the motion is:
The velocity-time graph for a particle moving along $x$-axis is shown in the figure. The corresponding displacement-time graph is correctly shown by
A bus moving along a straight highway with speed of $72 \mathrm{~km} / \mathrm{h}$ is brought to halt within $4 \mathrm{~s}$ after applying the brakes. The distance travelled by the bus during this time (Assume the retardation is uniform) is__________.$\mathrm{m}$.
A small pin fixed on a table top is viewed from above from a distance of $50\, cm$. By what distance would the pin appear to be raised if it is viewed from the same point through a $15\, cm$ thick glass slab held parallel to the table? Refractive index of glass $= 1.5$ ?......$cm$