Question

You've decided to protect your house by placing a7.0-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 45kA of current and last up to 50 ?s.Part AHow much charge is delivered by a lightning bolt with these parameters?Express your answer to two significant figures and include the appropriate units.Part BYou don't want the potential difference between the top and bottom of the lightning rod to exceed 130V . What minimum diameter must the rod haveExpress your answer to two significant figures and include the appropriate units

Answer 1

The lightning bolt delivers a charge of 2.25 C. For the minimum diameter of the lighting rod, we need additional information about the rod's material properties and the relationship between resistance and diameter, which is not provided in the question.

Step-by-step explanation:

Part A: Calculating Charge Delivered by a Lightning Bolt

To find the amount of charge delivered by a lightning bolt, we use the formula Q = I × t, where Q is the charge in coulombs (C), I is the current in amperes (A), and t is the time in seconds (s). In this case, the lightning bolt carries up to 45,000 A (45 kA) of current and lasts up to 50 microseconds (50 × 10⁻⁶ s). Therefore, the charge delivered by the lightning bolt is:

Q = 45,000 A × 50 × 10⁻⁶ s = 2.25 C

Part B: Calculating the Minimum Diameter of the Lightning Rod

To ensure that the potential difference between the top and bottom of the lightning rod does not exceed 130V, we must consider the rod's resistance and the current passing through it. The resistance (R) can be calculated using Ohm's law, R = V/I, where V is the voltage, and I is the current. However, without detailed information about the resistivity of the material or the formula for resistance in terms of diameter, we cannot provide an exact answer for the required diameter. We would need additional formulas and constants, such as the resistivity of iron and the formula for resistance based on the conductor's dimensions, to calculate the minimum diameter of the rod.