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Assertion (A) : Radiation resistance of an antenna is equal to the value of hypothetical resistance, that dissipates an equal amount of power, when a current is applied to the antenna.

Reason (R) : Radiation resistance of a short Hertzian dipole is given by \(R_{r} = 40\,\pi^{2}\left(\dfrac{dl}{\lambda}\right)^{2}\) ohms.

  • A.Both (A) and (R) are true and (R) is the correct explanation of (A).
  • B.Both (A) and (R) are true, but (R) is not the correct explanation of (A).
  • C.(A) is true and (R) is false.
  • D.(A) is false and (R) is true.

Answer: C

The assertion is true and the reason is false, option (C). The radiation resistance of an antenna is defined as the value of a hypothetical resistance that would dissipate the same power as the antenna radiates when it carries the same current, so the assertion is correct. For a short Hertzian dipole, the radiation resistance is \(R_{r} = 80\pi^{2}\left(\dfrac{dl}{\lambda}\right)^{2}\) ohms, so the figure of 40 in the reason is wrong; 40 gives half of the true value. Options (A) and (B) accept the reason and option (D) rejects the assertion, which is the standard definition.

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