Question

The minimum size of an antenna for transmitting electromagnetic waves at 1500 MHz is

• A. 2 cm
• B. 5 cm
• C. 5 m
• D. 200 m

Hint:

Wavelength calculation: $\lambda = c/f$.
Speed of light $c \approx 3 \times 10^8$ m/s.
Ensure frequency is in Hz ($1 \text{ MHz} = 10^6 \text{ Hz}$).
For efficient radiation/reception, antenna size is typically a significant fraction of the wavelength, commonly $\lambda/4$ (quarter-wave antenna) or $\lambda/2$ (half-wave dipole). The "minimum size" often refers to the $\lambda/4$ guideline.

Answer 1

The Correct Option is B

For efficient transmission and reception of electromagnetic waves, the size of the antenna should generally be comparable to the wavelength ($\lambda$) of the waves being transmitted or received. A common rule of thumb for a minimum or practical size, especially for a simple dipole antenna, is that its length should be of the order of $\lambda/4$ or $\lambda/2$. The question asks for the "minimum size," which often relates to $\lambda/4$. First, calculate the wavelength ($\lambda$) of the electromagnetic waves. The relationship between wavelength ($\lambda$), frequency ($f$), and the speed of light ($c$) is $c = f\lambda$. So, $\lambda = \frac{c}{f}$. Given values: Frequency $f = 1500 \text{ MHz} = 1500 \times 10^6 \text{ Hz} = 1.5 \times 10^9 \text{ Hz}$. Speed of light $c = 3 \times 10^8 \text{ m/s}$. Calculate $\lambda$: $\lambda = \frac{3 \times 10^8 \text{ m/s}}{1.5 \times 10^9 \text{ Hz}} = \frac{3}{1.5} \times \frac{10^8}{10^9} \text{ m}$. $\frac{3}{1.5} = 2$. $\frac{10^8}{10^9} = 10^{-1} = 0.1$. So, $\lambda = 2 \times 0.1 \text{ m} = 0.2 \text{ m}$. Convert wavelength to centimeters: $\lambda = 0.2 \text{ m} \times 100 \frac{\text{cm}}{\text{m}} = 20 \text{ cm}$. Now, consider the minimum size of the antenna. A common practical minimum length for an efficient antenna (like a quarter-wave monopole or one arm of a half-wave dipole) is $\lambda/4$. Minimum size $\approx \frac{\lambda}{4}$. Minimum size $\approx \frac{20 \text{ cm}}{4} = 5 \text{ cm}$. This matches option (b). If the antenna were a half-wave dipole, its total length would be $\lambda/2 = 20 \text{ cm}/2 = 10 \text{ cm}$. The term "size" could refer to the characteristic dimension. For many antenna types, $\lambda/4$ is a key dimension. Given the options, 5 cm is a strong candidate. \[ \boxed{5 \text{ cm}} \]