   Chapter 18, Problem 57AP

Chapter
Section
Textbook Problem

The student engineer of a campus radio station wishes to verify the effectiveness of the lightning rod on the antenna mast (fig. P18.57). the unknown resistance R x 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 R y The procedure for the unknown resistance R x is as follows. Measure resistsnce R 1 between points A and B Then Connect A and B with a heavy conducting wire and measure resistance R 2 between points A and C. (a) Derive a formula For R x in terms of the observable resistances R 1 and R 2 (b) A satisfactory ground resistance would be R x   <2 .0Ω   Is the grounding of the sation adequate if measurements give R 1 =13Ω   and   R 2 =6 .0Ω? To determine
The resistance between the points a and b is, Rab=2717Ω .

Explanation

Given info:

Explanation:

Connect a battery of emf ε between the points a and b.

On applying the Kirchhoff’s rule in the loop acbea,

(1.0)I1(1.0)(I1I3)+ε=0

On re-arranging,

I3=2I1ε (I)

On applying the Kirchhoff’s rule in the loop adbea,

(3.0)I2(5.0)(I2+I3)+ε=0

On re-arranging,

8I2+5I3=ε (II)

On applying the Kirchhoff’s rule in the loop abca,

(3.0)I2+(1.0)I3+(1.0)I1=0

On re-arranging,

I2=I1+I33 (III)

Substitute the equation (I) in (III),

I2=I1+(2I1ε)3=I1ε3 (IV)

Substitute the equations (I) and (IV) in (II),

8(I1ε3)+5(2I1ε

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