This physics problem tests your understanding of fundamental physical laws and their applications. The step-by-step solution below breaks down the problem using relevant equations and physical reasoning.
ScanSolve AI Answer
Here's the solution for calculating the received power based on your image: The problem asks to calculate the received power (P_R) under two conditions using the provided data. Given Data: • Distance d = 2000 m • Transmitter height h_t = 20 m • Receiver height h_r = 1 m • Transmission Frequency F = 1 GHz = 1 × 10^9 Hz • Transmitter Gain G_t = 10 • Receiver Gain G_r = 5 • Power transmitted P_t = 2 W Step 1: Calculate the wavelength (). The speed of light c = 3 × 10^8 m/s. = (c)/(F) = 3 × 10^8 m/s1 × 10^9 Hz = 0.3 m Step 2: Calculate the received power (P_R) neglecting reflections (using the Friis transmission formula). The formula is: P_R = P_t G_t G_r (()/(4 d))^2 Substitute the given values: P_R = (2 W) × 10 × 5 × (0.3 m4 × 2000 m)^2 P_R = 100 W × ((0.3)/(25132.74))^2 P_R = 100 W × (1.19366 × 10^-5)^2 P_R = 100 W × (1.4248 × 10^-10) P_R = 1.4248 × 10^-8 W Converting to nanowatts (nW): P_R = 1.4248 × 10^-8 W × 10^9 nW1 W P_R = 14.248 nW The received power neglecting reflections is 14.2 nW. Step 3: Calculate the received power (P_R) including reflections (using the two-ray ground reflection model). The formula is: P_R = P_t G_t G_r ((h_t h_r)/(d^2))^2 Substitute the given values: P_R = (2 W) × 10 × 5 × (20 m × 1 m(2000 m)^2)^2 P_R = 100 W × ((20)/(4000000))^2 P_R = 100 W × (5 × 10^-6)^2 P_R = 100 W × (25 × 10^-12) P_R = 2500 × 10^-12 W P_R = 2.5 × 10^-9 W Converting to nanowatts (nW): P_R = 2.5 × 10^-9 W × 10^9 nW1 W P_R = 2.5 nW The received power including reflections is 2.5 nW. 3 done, 2 left today. You're making progress.