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Chapter 20: Problem 2

An especially violent lightning bolt has an average current of \(1.26 \times 10^{3}\) A lasting 0.138 s. How much charge is delivered to the ground by the lightning bolt?

Short Answer

Expert verified
173.88 coulombs are delivered to the ground by the lightning bolt.

Step by step solution

01

Understanding the Relationship between Current, Charge, and Time

The relationship between current, charge, and time is given by the equation \( Q = I \times t \), where \( Q \) is the electric charge, \( I \) is the current, and \( t \) is the time. This equation helps us calculate the total charge delivered by a current over a specific time interval.
02

Identify Given Values

From the problem statement, we identify the given values: Current \( I = 1.26 \times 10^3 \) A, and Time \( t = 0.138 \) seconds. We will use these values in the formula to find the charge.
03

Substitute the Given Values into the Equation

Substitute \( I = 1.26 \times 10^3 \) A and \( t = 0.138 \) s into the equation \( Q = I \times t \). This results in: \( Q = (1.26 \times 10^3) \times 0.138 \).
04

Calculate the Charge

Perform the multiplication to find the charge: \( Q = 1.26 \times 10^3 \times 0.138 = 173.88 \). Therefore, the charge delivered is \( 173.88 \) coulombs.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Current and Charge Relationship
Electric charge and current are two fundamental concepts that are closely related in the study of electricity. Understanding their relationship forms the basis for analyzing electrical systems.
  • Electric Charge: Charge is a fundamental property of particles like electrons and protons. It is measured in coulombs (C).
  • Electric Current: Current is the rate at which charge flows through a conductor. It is measured in amperes (A), where 1 ampere represents 1 coulomb of charge passing a point per second.
The relationship between current, charge, and time is captured by the formula: \[ Q = I imes t \]where \(Q\) is the total charge, \(I\) is the current, and \(t\) is the time. This equation shows that the total charge transferred over a period is simply the product of the current and the time duration.
Current Equation
The current equation, \( Q = I \times t \), is crucial in calculating how much charge is transferred in any given electrical process. Let's break down what each component represents in simple terms:
  • Q (Charge): The total charge transferred, measured in coulombs (C).
  • I (Current): The flow of electric charge, measured in amperes (A).
  • t (Time): The duration over which the current flows, measured in seconds (s).
By substituting known values of current and time into the equation, you can easily compute the charge. This step-by-step approach helps ensure you understand the relationship between these variables and apply it correctly in exercises.
Electric Current Calculation
When you calculate electric current, you're essentially solving how much charge moves through a system in a specific period of time. To perform the calculation:
  • Begin by identifying the current and how long it flows.
  • Use the relationship \( Q = I \times t \) to calculate the charge.
  • Multiply the current by the time to find the total charge transferred.
In the given lightning exercise, a current of \(1.26 \times 10^3\) amperes over \(0.138\) seconds results in a charge of \(173.88\) coulombs transferred to the ground. Breaking down the multiplication step by step helps to ensure accuracy and deepen comprehension of how current calculations are conducted.
Lightning and Electricity
Lightning is a natural electrical discharge phenomenon that occurs during thunderstorms. It is a prime example of the immense power of electricity in nature.
Lightning bolts can range from a few hundred to over a thousand amperes, indicating how strong and violent these electric currents can be. The vast quantities of charge moved by lightning can heat the surrounding air up to temperatures hotter than the sun's surface, which is why lightning strikes are so bright and powerful.
  • Connection to Electric Current: Lightning serves as a massive natural demonstration of electric current and charge transfer. The same principles you use to calculate the charge moved by a small circuit are applicable to understanding lightning.
  • Practical Implications: Understanding how to calculate the charge involved in lightning strikes is vital for building protection systems on structures, helping to prevent damage from these powerful natural events.
Thus, studying lightning not only informs atmospheric science but also advances safety engineering.

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