A C B R, R, Figure P27.49
The student engineer of a campus radio station wishes to verify the effectiveness of the lightning rod on the antenna mast (as shown). The unknown resistance Rx 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 Ry. 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 Rx in terms of the observable resistances, R1 and R2. (b) A satisfactory ground resistance would be Rx < 2.00 Ω. Is the grounding of the station adequate if measurements give R1 = 13.0 Ω and R2 = 6.00 Ω? Explain.
Given data:
The unknown resistance between point C and E is: Rx.
The unknown resistance between point A and B is: Ry.
The given figure can be redrawn as,
The value of R1 is given as,
The value of R2 is given as,
The expression for Rx is given as,
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