Chapter 27, Problem 027 Flying Circus of Physics The figure indicates one reason

Question

Chapter 27, Problem 027 Flying Circus of Physics The figure indicates one reason no one should stand under a tree during a lightning storm. If lightning comes down the side of the tree, a portion can jump over to the person, especially if the current on the tree reaches a dry region on the bark and thereafter must travel through air to reach the ground. In the figure, part of the lightning jumps through distance d in air and then travels through the person (who has negligible resistance relative to that of air). The rest of the current travels through air alongside the tree, for a distance h. If d/-0.431 and the total current is I - 5260 A, what is the current through the person? Lighming current Number Units the tolerance is +/-296

Explanation / Answer

We have to condsider the two paths as having resistances R1and R2 proportional to the length of the path(air). The resistanceof the man is negligible.

So we have two resistors in parallel between A and B (ground).

Let I1 and I2 be the current through the man and through the tree respectively.

                  VAB = I1*R1 = I2*R2

                  R1/R2 = I2/I1

Also R is proportional to length of air path

                 R1/R2 = d/h

R1/R2 = 0.431

Hence,  I2/I1 = R1/R2

              I2/I1 = 0.431   

Then the current  I2  = 0.431* I1

But          I2 +I1 = 5260 A

Combining, I1 + 0.431* I1 = 5260

                         I1 = 5260 /1.431

I1 = 3675.75 A

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