Question

A 1-m-long monopole car radio antenna operates in the AM frequency of 1.5 MHz. How muchcurrent is required to transmit 4 W of power?

Answer 1

The current needed to transmit Power of 4 W is 28.47 A

Solution:

As per the question:

Length of the antenna,
`L_(a) = 1 m`

Frequency,
`\vartheta = 1.5 MHz = 1.5* 10^(6) Hz`

Power transmitted,
`P_(t) = 4 W`

Now,

For a monopole antenna:

`\lambda_(a) = (c)/(\vartheta)`

where

`\lambda_(a)` = wavelength transmitted by the antenna

c = speed of light in vacuum

`\lambda_(a) = (3* 10^(8))/(1.5* 10^(6)) = 200 m`

Now,

Since, the value of
`\lambda_(a)` >>
`L_(a)` thus the monopole is a Hertian monopole.

The resistance is calculated as:

`R = (1)/(2)((dL_(a))/(\lambda_(a)))^(2)* 80\pi^(2)`

`P_(radiated) = P_(t)`

`P_(radiated) = (R)/(I^(2))`

Now, the current I is given by:

`I = \sqrt{(2P_(t))/(R)} = \sqrt{(2* 4)/(9.869* 10^(- 3))} = 28.47 A`