Electron Flow In Electric Device Problem And Solution

by Sharif Sakr 54 views

Hey physics enthusiasts! Ever wondered about the tiny particles zipping through your electronic devices? We're talking about electrons, the unsung heroes of our digital world. In this article, we are going to dive into a fascinating problem that combines the concepts of electric current and electron flow. Let's unravel the mystery of how to calculate the number of electrons that flow through a device given the current and time. So, grab your thinking caps, and let’s get started!

Understanding Electric Current

Before we dive into the problem, let's brush up on some fundamental concepts. What exactly is electric current? In simple terms, electric current is the flow of electric charge. Think of it like water flowing through a pipe; the more water that flows per unit time, the higher the current. In the case of electricity, the charge carriers are usually electrons, those negatively charged particles that orbit the nucleus of an atom. When these electrons move in a specific direction, they create an electric current. The standard unit for measuring electric current is the ampere (A), named after the French physicist André-Marie Ampère. One ampere is defined as one coulomb of charge flowing per second (1 A = 1 C/s). This means that if you have a current of 15.0 A, it's like having 15.0 coulombs of charge flowing through the device every second. Now, you might be wondering, what's a coulomb? A coulomb (C) is the unit of electric charge. It's a pretty large unit, actually. One coulomb is approximately equal to the charge of 6.242 × 10^18 electrons. This massive number highlights just how many electrons are constantly on the move in even a small electric current. So, when we talk about a current of 15.0 A, we're talking about an incredibly large number of electrons flowing through the device every second. Electric current is not just a simple flow; it’s a coordinated movement of a vast number of electrons. This flow is driven by an electric field, which is created by a voltage source, like a battery or a power outlet. The electrons, being negatively charged, are attracted to the positive terminal and repelled by the negative terminal, causing them to move through the circuit. The magnitude of the current depends on both the voltage and the resistance of the circuit. Higher voltage means a stronger push on the electrons, leading to a higher current, while higher resistance means more opposition to the flow, leading to a lower current. The relationship between voltage (V), current (I), and resistance (R) is described by Ohm's Law: V = IR. This fundamental law is the cornerstone of circuit analysis and helps us understand how electrical devices behave. So, in summary, electric current is the flow of electric charge, typically electrons, measured in amperes. It’s a crucial concept for understanding how our electronic devices work, from the simplest light bulb to the most complex computer. With this understanding, we can now tackle the problem of calculating the number of electrons flowing through a device given the current and time.

Problem Statement and Approach

Now that we have a solid grasp of electric current, let's tackle the problem at hand. The question asks: An electric device delivers a current of 15.0 A for 30 seconds. How many electrons flow through it? This is a classic physics problem that bridges the concepts of current, charge, and the fundamental charge of an electron. To solve this, we need to connect the given information (current and time) to the quantity we want to find (number of electrons). Here's the breakdown of our approach:

  1. Relate current and charge: We know that current (I) is the rate of flow of charge (Q) over time (t). Mathematically, this is expressed as I = Q/t. This equation is our starting point because it directly links the given current and time to the charge that has flowed through the device.
  2. Calculate the total charge: Using the given current of 15.0 A and the time of 30 seconds, we can rearrange the equation to solve for the total charge (Q). So, Q = I * t. This will give us the total charge in coulombs that has passed through the device during the 30-second interval.
  3. Relate charge and number of electrons: We know that the charge of a single electron is approximately 1.602 × 10^-19 coulombs. This is a fundamental constant in physics and is often denoted by the symbol 'e'. To find the number of electrons (n) that make up the total charge (Q), we divide the total charge by the charge of a single electron: n = Q / e. This step will give us the number of electrons that have flowed through the device.
  4. Putting it all together: By combining these steps, we can calculate the number of electrons that flowed through the device. We first use the current and time to find the total charge, and then we use the total charge and the charge of a single electron to find the number of electrons. This approach is straightforward and relies on fundamental physics principles. It's a great example of how we can use basic equations to solve practical problems. Before we jump into the calculations, let's make sure we understand the logic behind each step. We are essentially converting the current, which is a rate of charge flow, into a total charge by considering the time interval. Then, we are converting the total charge into a number of electrons by using the fundamental charge of an electron as a conversion factor. This problem-solving strategy is widely applicable in physics and engineering, where we often need to relate macroscopic quantities (like current) to microscopic quantities (like the number of electrons).

Step-by-Step Solution

Alright, guys, let's get down to the nitty-gritty and solve this problem step by step. We've already laid out the plan, so now it's time to put those equations into action. Remember, we're trying to find out how many electrons flow through an electric device when it delivers a current of 15.0 A for 30 seconds. Here's how we'll do it:

Step 1: Relate Current and Charge

We start with the fundamental relationship between current (I), charge (Q), and time (t): I = Q/t. This equation tells us that the current is the amount of charge flowing per unit time. In our case, we know the current (I = 15.0 A) and the time (t = 30 s), and we want to find the total charge (Q). So, we need to rearrange the equation to solve for Q. Multiplying both sides of the equation by t, we get: Q = I * t This is our working equation for this step. It's a simple rearrangement, but it's crucial for connecting the given information to the quantity we want to find. By understanding this relationship, we can move forward with confidence.

Step 2: Calculate the Total Charge

Now that we have our equation, Q = I * t, we can plug in the given values. The current (I) is 15.0 A, and the time (t) is 30 seconds. So, Q = 15.0 A * 30 s Remember that 1 ampere is equal to 1 coulomb per second (1 A = 1 C/s). Therefore, when we multiply amperes by seconds, we get coulombs. Performing the calculation: Q = 15.0 C/s * 30 s = 450 C So, the total charge that flows through the device in 30 seconds is 450 coulombs. That's a lot of charge! But remember, a coulomb is a large unit, representing the charge of about 6.242 × 10^18 electrons. We're getting closer to our final answer. We've now found the total charge, which is the bridge between the current and the number of electrons.

Step 3: Relate Charge and Number of Electrons

The next step is to connect the total charge (Q) to the number of electrons (n). We know that each electron carries a charge of approximately 1.602 × 10^-19 coulombs. This is a fundamental constant, often denoted by 'e'. To find the number of electrons that make up the total charge of 450 coulombs, we divide the total charge by the charge of a single electron: n = Q / e Plugging in the values: n = 450 C / (1.602 × 10^-19 C/electron) This equation tells us how many electrons are needed to make up the 450 coulombs of charge that flowed through the device. It's like saying,