What will be the minimum length of antenna required to transmit a radio signal of frequency 10 MHz?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 7.5 m
An antenna radiates effectively only if its size is comparable to the wavelength of the signal, and the minimum length is \( \lambda/4 \). First find the wavelength from \( c = f\lambda \).
\( \displaystyle \lambda = \frac{c}{f} = \frac{3\times10^{8}}{10\times10^{6}}\,\mathrm{m} = 30\,\mathrm{m} \)
\( \displaystyle l_{\min} = \frac{\lambda}{4} = \frac{30}{4}\,\mathrm{m} = 7.5\,\mathrm{m} \)
Note: This question is from the pre-rationalised NCERT book (2022-23). The topic was removed from the latest NCERT book (2026-27), and it also appears to be out of the CUET 2026 syllabus.
NCERT (Pre-rationalised edition, 2022-23):
Size of the Antenna or Aerial – “For transmitting a signal, we need an antenna or an aerial. This antenna should have a size comparable to the wavelength of the signal (at least λ/4 in dimension) so that the antenna properly senses the time variation of the signal.”