Answer:
The current needed to transmit Power of 4 W is 28.47 A
Solution:
As per the question:
Length of the antenna, [tex]L_{a} = 1 m[/tex]
Frequency, [tex]\vartheta = 1.5 MHz = 1.5\times 10^{6} Hz[/tex]
Power transmitted, [tex]P_{t} = 4 W[/tex]
Now,
For a monopole antenna:
[tex]\lambda_{a} = \frac{c}{\vartheta}[/tex]
where
[tex]\lambda_{a}[/tex] = wavelength transmitted by the antenna
c = speed of light in vacuum
[tex]\lambda_{a} = \frac{3\times 10^{8}}{1.5\times 10^{6}} = 200 m[/tex]
Now,
Since, the value of [tex]\lambda_{a}[/tex] >> [tex]L_{a}[/tex] thus the monopole is a Hertian monopole.
The resistance is calculated as:
[tex]R = \frac{1}{2}(\frac{dL_{a}}{\lambda_{a}})^{2}\times 80\pi^{2}[/tex]
[tex]R = \frac{1}{2}(\frac{1}{200)^{2}\times 80\pi^{2} = 9.869\times 10^{- 3} = 9.869 m\Omega[/tex]
[tex]P_{radiated} = P_{t}[/tex]
[tex]P_{radiated} = \frac{R}{I^{2}}[/tex]
Now, the current I is given by:
[tex]I = \sqrt{\frac{2P_{t}}{R}} = \sqrt{\frac{2\times 4}{9.869\times 10^{- 3}}} = 28.47 A[/tex]
