Question:
The minimum size of an antenna for transmitting electromagnetic waves at \(1500\ \text{MHz}\) is
The minimum size of an antenna for transmitting electromagnetic waves at \(1500\ \text{MHz}\) is
Show Hint
For transmission and reception of electromagnetic waves, the minimum practical antenna length is approximately
\[
L=\frac{\lambda}{4}.
\]
First calculate the wavelength using
\[
\lambda=\frac{c}{f},
\]
and then divide by 4.
Updated On: Jun 26, 2026
- \(2\ \text{cm}\)
- \(5\ \text{cm}\)
- \(5\ \text{m}\)
- \(200\ \text{m}\)
Show Solution
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The Correct Option is B
Solution and Explanation
Step 1: Use the relation between wavelength and frequency.
The wavelength of the electromagnetic wave is \[ \lambda=\frac{c}{f}, \] where \[ c=3\times10^8\ \text{m s}^{-1} \] and \[ f=1500\ \text{MHz} =1500\times10^6\ \text{Hz} =1.5\times10^9\ \text{Hz}. \] Thus, \[ \lambda = \frac{3\times10^8}{1.5\times10^9}. \] \[ \lambda = 2\times10^{-1}\ \text{m}. \] \[ \lambda = 0.2\ \text{m} = 20\ \text{cm}. \]
Step 2: Determine the minimum antenna length.
For efficient transmission, the minimum length of an antenna is approximately \[ L=\frac{\lambda}{4}. \] Therefore, \[ L=\frac{20}{4}\ \text{cm}. \] \[ L=5\ \text{cm}. \]
Step 3: Final conclusion.
Hence, the minimum size of the antenna is \[ \boxed{5\ \text{cm}} \] Therefore, the correct option is \[ \boxed{(2)} \]
The wavelength of the electromagnetic wave is \[ \lambda=\frac{c}{f}, \] where \[ c=3\times10^8\ \text{m s}^{-1} \] and \[ f=1500\ \text{MHz} =1500\times10^6\ \text{Hz} =1.5\times10^9\ \text{Hz}. \] Thus, \[ \lambda = \frac{3\times10^8}{1.5\times10^9}. \] \[ \lambda = 2\times10^{-1}\ \text{m}. \] \[ \lambda = 0.2\ \text{m} = 20\ \text{cm}. \]
Step 2: Determine the minimum antenna length.
For efficient transmission, the minimum length of an antenna is approximately \[ L=\frac{\lambda}{4}. \] Therefore, \[ L=\frac{20}{4}\ \text{cm}. \] \[ L=5\ \text{cm}. \]
Step 3: Final conclusion.
Hence, the minimum size of the antenna is \[ \boxed{5\ \text{cm}} \] Therefore, the correct option is \[ \boxed{(2)} \]
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