Question

If a linear antenna radiates a power \(P\) at a wavelength \(\lambda\), then the power radiated by the same antenna at a wavelength of \(\frac{\lambda}{\sqrt{3}}\) is:

• A. \(P\)
• B. \(\sqrt{3} P\)
• C. \(\frac{P}{3}\)
• D. \(3P\)

Hint:

For antennas, power radiated varies inversely with the square of the wavelength. Reducing the wavelength increases the power radiated accordingly.

Answer 1

The Correct Option is D

Power radiated by a linear antenna is inversely proportional to the square of the wavelength, i.e., \[ P \propto \frac{1}{\lambda^2} \] Given the original power is \(P\) at wavelength \(\lambda\). At wavelength \(\frac{\lambda}{\sqrt{3}}\), the power radiated \(P'\) is: \[ P' = P \times \left(\frac{\lambda}{\frac{\lambda}{\sqrt{3}}}\right)^2 = P \times (\sqrt{3})^2 = 3P \] Thus, the power radiated at \(\frac{\lambda}{\sqrt{3}}\) is \(3P\).