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GATE 2026 EC – Question 21

Electromagnetics · Antennas and Antenna Arrays · 1 mark · Multiple choice

Consider the Friis’ transmission equation $P_R=(P_TG_TG_R\lambda^2)/(4\pi D)^2$, 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: $G_T=G_R=1.0$, $\lambda=0.30$ m and $P_T=+10$ dBm. Choose the distance ($D$), in km, from the following options at which the received power, $P_R=-90$ dBm?

  1. $\frac{15}{4\pi}$
  2. $\frac{15}{2\pi}$
  3. $\frac{75}{2\pi}$
  4. $\frac{3}{4\pi}$

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Correct answer: (B) $\frac{15}{2\pi}$

Explanation

The path loss is $10-(-90)=100$ dB, so $(\lambda/4\pi D)^2=10^{-10}$ and $D=\lambda\times10^5/(4\pi)=30000/(4\pi)$ m $=15/(2\pi)$ km.