You\'ve decided to protect your house by placing a 6.8-m-tall iron lightning rod

Question

You've decided to protect your house by placing a 6.8-m-tall iron lightning rod next to the house. The top is sharpened to a point and the bottom is in good contact with the ground. From your research, you've learned that lightning bolts can carry up to 49 kA of current and last up to 50 s.

Part A

How much charge is delivered by a lightning bolt with these parameters?

Express your answer to two significant figures and include the appropriate units.

Part B

You don't want the potential difference between the top and bottom of the lightning rod to exceed 100 V . What minimum diameter must the rod have

Express your answer to two significant figures and include the appropriate units.

Explanation / Answer

PART A

Q=It The current is given in kA so I=49,000A. Time is in µs so t=5*10^-5
Q=(49000)(5.0*10^-5)=2.45C

PART B
R=pL/A
R=Resistance p=resistivity L=Length A=Cross-sectional area(r^2)
The resistivity of iron is 9.7*10^-8 m

The minimum resistance is equal to the minimum Potential difference divided by the current
V/I=Rmin -> 100V/49000A=0.00204


rearranging the Resistance equation to solve for r, r=(pL/Rmin*)^(1/2)
[(9.7*10^-8)(6.8m)/(0.00204)]^(1/2) = 0.0101

d=r*2 d=0.0202m d=2.02cm

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