Chapter 28, Problem 28.77AP

The student engineer of a campus radio station wishes to verify the effectiveness of the lightning rod on the antenna mast (Fig. P27.49). The unknown resistance R_x is between points C and E. Point E is a true ground, but it is inaccessible for direct measurement because this stratum is several meters below the Earth’s surface. Two identical rods are driven into the ground at A and B, introducing an unknown resistance R_y. The procedure is as follows. Measure resistance R₁ between points A and B, then connect A and B with a heavy conducting wire and measure resistance R₂ between points A and C. (a) Derive an equation for R_x in terms of the observable resistances, R₁, and R₂. (b) A satisfactory ground resistance would R_x < 2.00 Ω. Is the grounding of the station adequate if measurements give R₁ = 13.0 Ω and R₂ = 6.00 Ω? Explain.

Figure P27.49