GATE EC 2026 Set 1 Q11 — Transmission Lines

Consider the Friis' transmission equation $P_{R}=\left(P_{T} G_{T} G_{R} \lambda^{2}\right) /(4 \pi D)^{2}$, where $P_{R}$ and $P_{T}$ are the received and the transmitted powers, respectively. $G_{T}$ and $G_{R}$ are the gain of transmitting and receiving antennas, respectively, $D$ is the distance between the transmitting and receiving antennas, and $\lambda$ is the wavelength in free space.

Given: $G_{T}=G_{R}=1.0, \lambda=0.30 \mathrm{~m}$ and $P_{T}=+10 \mathrm{dBm}$.

Choose the distance ( $D$ ), in km, from the following options at which the received power, $P_{R}=-90 \mathrm{dBm}?$