Electrons Flow: 15.0 A Current In 30 Seconds

by Rajiv Sharma 45 views

Hey guys! Ever wondered how many tiny electrons zip through your electronic devices every time you switch them on? Well, today we're diving into a cool physics problem that helps us figure out exactly that. We're going to calculate the number of electrons flowing through an electric device given the current and time. Let's get started!

Understanding the Basics

Before we jump into the calculation, let's quickly recap some key concepts. Electric current is essentially the flow of electric charge, typically carried by electrons, through a conductor. We measure current in amperes (A), where 1 ampere represents 1 coulomb of charge flowing per second. Think of it like water flowing through a pipe; the current is the amount of water passing a certain point every second.

The fundamental unit of charge is the charge of a single electron, denoted as 'e'. The value of 'e' is approximately $1.602 \times 10^{-19}$ coulombs. This tiny number represents the amount of charge one electron carries. Now, to relate current, time, and the number of electrons, we use the following formula:

Q=I×t Q = I \times t

Where:

  • Q is the total charge (in coulombs)
  • I is the current (in amperes)
  • t is the time (in seconds)

This equation tells us that the total charge flowing through a device is equal to the current multiplied by the time it flows. But we're not just interested in the total charge; we want to know how many electrons make up that charge. For this, we use another simple relation:

N=Qe N = \frac{Q}{e}

Where:

  • N is the number of electrons
  • Q is the total charge (in coulombs)
  • e is the charge of a single electron ($1.602 \times 10^{-19}$ coulombs)

This equation simply divides the total charge by the charge of a single electron to give us the number of electrons.

Problem Setup

Now, let's apply these concepts to our specific problem. We have an electric device that delivers a current of 15.0 A for 30 seconds. Our goal is to find the number of electrons that flow through the device during this time. To solve this, we'll follow a step-by-step approach, using the formulas we just discussed.

First, we identify the given values:

  • Current (I) = 15.0 A
  • Time (t) = 30 seconds

We also know the charge of a single electron:

  • e = $1.602 \times 10^{-19}$ coulombs

Next, we'll calculate the total charge (Q) using the formula $ Q = I \times t $. After that, we'll use the total charge to find the number of electrons (N) using the formula $ N = \frac{Q}{e} $. Let's dive into the calculations!

Calculating the Total Charge

The first step in solving our problem is to calculate the total charge (Q) that flows through the electric device. We know the current (I) is 15.0 A, and the time (t) is 30 seconds. Using the formula:

Q=I×t Q = I \times t

We can plug in the values:

Q=15.0 A×30 s Q = 15.0 \text{ A} \times 30 \text{ s}

Multiplying these values gives us:

Q=450 coulombs Q = 450 \text{ coulombs}

So, the total charge that flows through the device in 30 seconds is 450 coulombs. This is a significant amount of charge, but remember, it's made up of countless tiny electrons. Now that we have the total charge, we can move on to the next step: calculating the number of electrons.

Determining the Number of Electrons

Now that we've calculated the total charge (Q), we can find the number of electrons (N) that flowed through the device. We know the total charge is 450 coulombs, and the charge of a single electron (e) is $1.602 \times 10^{-19}$ coulombs. We'll use the formula:

N=Qe N = \frac{Q}{e}

Plugging in the values, we get:

N=450 coulombs1.602×10−19 coulombs/electron N = \frac{450 \text{ coulombs}}{1.602 \times 10^{-19} \text{ coulombs/electron}}

This calculation involves dividing a relatively large number (450) by a very small number ($1.602 \times 10^{-19}$). When we perform this division, we get:

N≈2.81×1021 electrons N \approx 2.81 \times 10^{21} \text{ electrons}

This is a massive number! It means that approximately 2.81 sextillion electrons flow through the device in 30 seconds. To put this into perspective, a sextillion is 10 to the power of 21, which is a 1 followed by 21 zeros. That's an incredibly large number of tiny particles zipping through the device.

Conclusion

So, to answer our original question, approximately 2.81 x 10^21 electrons flow through the electric device when a current of 15.0 A is delivered for 30 seconds. Isn't it mind-blowing to think about the sheer number of electrons involved in even a simple electrical process? This calculation highlights the immense scale of the microscopic world and how it governs the macroscopic phenomena we observe.

We've successfully walked through the problem, applying the fundamental principles of electric current and charge. Remember, the key formulas we used were:

  • Q=I×t Q = I \times t

  • N=Qe N = \frac{Q}{e}

Understanding these relationships allows us to analyze and predict the behavior of electrical systems. Keep exploring the fascinating world of physics, guys, and you'll uncover even more amazing insights!