The student engineer of a campus radio station wishes to verify the effectivencess of the lightning rod on the antenna mast.

Reggie

Reggie

Answered question

2021-05-18

The student engineer of a campus radio station wishes to verify the effectivencess of the lightning rod on the antenna mast. The unknown resistance Rx is between points C and E. Point E is a "true ground", but is inaccessible for direct measurement because the stratum in which it is located is several meters below Earth's surface. Two identical rods are driven into the ground at A and B, introducing an unknown resistance Ry. The procedure for finding the unknown resistance Rx 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.Derive a formula for Rx in terms of the observable resistances R1 and R2. A satisfactory ground resistance would be Rx<2.0 Ohms. Is the grounding of the station adequate if measurments give R1=13Ohms and R2=6.0 Ohms?

Answer & Explanation

diskusje5

diskusje5

Skilled2021-05-20Added 82 answers

a) Two identical rods are driven into the ground at A and B, introducing an unknown resistance Ry. The procedure for finding the unknown resistance Rx 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. This shown in below figure.
image
The equivalent resistance of series resistors Ry and Ry is
R1=Ry+Ry
=2Ry
image
From the above circuit Ry and Ry are connected in parallel. The equivalent resistance is
Req=[1Ry+1Ry]1
=Ry2
And, Req and Rx are connected in series. Then the equivalent resistance is
R2=Req+Rx
=Ry2+Rx
From (1),
Ry=R12
Substitute this value in equation, we get
R2=12(R12)+Rx
=R14+Rx
Rx=R2R14
b) If the measurement give R1=13 Ohm and R2=6.0 Ohm
Then
Rx=R2R14
=(6.0 Ohm)(13 Ohm4)
=2.75 Ohm
2.8 Ohm
Here satisfactory ground resistance would be Rx<2.0 Ohm. So Rx is exceeds the limit of 2.0 Ohm
Therefore, the antenna is not adequate grounded.

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