Question

For efficient transmission of a $100MHz$ frequency wave, the minimum length of an antenna should be

• A. $3m$
• B. $\frac{3}{4}m$
• C. $10m$
• D. $100m$

Answer 1

The correct option is B

$\frac{3}{4}m$

Step 1. Given Data,

Frequency $f=100MHz$

Minimum Length $l=?$

Step 2. We have to calculate the minimum Length $l,$

Length of the antenna $l=\left(\frac{1}{4}\right)\times wavelength$

We know that wavelength, $\lambda =\frac{c}{f}$

$$\begin{gathered} \Rightarrow \lambda =\frac{\left(3\times {10}^8\right)m{s}^{-1}}{\left(100\times {10}^6\right)Hz} \\ \Rightarrow \lambda =3m \end{gathered}$$

Therefore, $l=\left(\frac{1}{4}\right)\times 3m$

$\Rightarrow l=\left(\frac{3}{4}\right)m$

Length of the antenna $l=\left(\frac{3}{4}\right)m$.

Hence, correct option is $\text{'}B\text{'}$,