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Ch 27: Current and Resistance
Knight Calc - Physics for Scientists and Engineers 5th Edition
Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796Non è quello che usi tu?Cambia libro di testo
Tutti i libri di testoKnight Calc 5th EditionCh 27: Current and ResistanceProblema 65a
Capitolo 27, Problema 65a

You've decided to protect your house by placing a 5.0-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 50 kA of current and last up to 50 μs. How much charge is delivered by a lightning bolt with these parameters?

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Identify the given values: The current carried by the lightning bolt is \( I = 50 \text{kA} = 50,000 \text{A} \), and the duration of the lightning bolt is \( t = 50 \mu\text{s} = 50 \times 10^{-6} \text{s} \).
Recall the relationship between charge, current, and time: \( Q = I \cdot t \), where \( Q \) is the charge, \( I \) is the current, and \( t \) is the time.
Substitute the given values into the formula: \( Q = (50,000 \text{A}) \cdot (50 \times 10^{-6} \text{s}) \).
Simplify the expression by multiplying the current and time to calculate the total charge delivered by the lightning bolt.
Express the result in coulombs (C), as charge is measured in this unit, and ensure the final value is in proper scientific notation if necessary.

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Current

Current is the flow of electric charge in a circuit, measured in amperes (A). In the context of lightning, the current can be extremely high, as indicated by the 50 kA mentioned in the question. This high current results from the rapid movement of electrons during a lightning strike, which can deliver a significant amount of energy in a very short time.
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Intro to Current

Charge

Electric charge is a fundamental property of matter that causes it to experience a force when placed in an electromagnetic field. Charge is measured in coulombs (C). The total charge delivered by a lightning bolt can be calculated using the formula Q = I × t, where Q is the charge, I is the current, and t is the time duration of the current flow.
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Charging Objects

Time Duration

Time duration refers to the length of time that an event occurs. In the case of a lightning strike, the duration is typically very short, often in the microsecond range, as indicated by the 50 μs in the question. This brief time frame is crucial for calculating the total charge delivered, as it directly influences the amount of charge that flows during the lightning event.
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Velocity-Time Graphs & Acceleration
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You've decided to protect your house by placing a 5.0-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 50 kA of current and last up to 50 μs. 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?

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