Question

A lightning bolt strikes one end of a steel lightning rod, producing a 14500-A current burst that lasts for 65 . The rod is 2.5 long and 2.1 in diameter, and its other end is connected to the ground by 38 of 8.1-mm-diameter copper wire.

A.Find the potential difference between the top of the steel rod and the lower end of the copper wire during the current burst.
(answer in volts, V)
B.Find the total energy deposited in the rod and wire by the current burst.
(answer in joules, J)
Either or

Answer 1

a. 206.9v

b. 194.7J

Step-by-step explanation:

Data given

`current, I=14500A\\time,t=65*10^(-6)sec\\lenght of steel L_(1)=2.5m,\\Radius of steel R_(1)=1.05cm=0.0105m\\Area=\pi R^(2)=0.000346m^(2)\\lenght of copper L_(2)=38m,\\Radius of copper R_(2)=4.05mm=0.00405m\\Area=\pi R^(2)=0.0000515m^(2)\\`

Next we calculate the resistance for each metal

since
`R=pA/L`

for steel, p=20*10^-8 ohmmeter

for copper, p=1.72*10^-8 ohmmeter

if we substitute values we arrive at

`R_(steel)=0.00145 ohms\\R_(copper)=0.0128 ohms\\`

The potential difference is expressed as

`V=I(R_(steel)+R_(copper))\\V=14500(0.00145+0.0128)\\V=206.9v`

b. using the equation for energy, we have

`E=I^(2)Rt\\E=14500*(0.00145+0.0128)*65*10^(-6)\\E=194.7J`