The current supplied by a battery as a function of time is I(t) = Ioe i/T where Io =4.68 A and T =22.7s. Determine the total number of electrons transported from the positive electrode to the negative electrode from the time the battery is first used until it is essentially dead (t = ∞0). (in E electrons, where E = Exa = 1018) I want show all work look at correct answer
The current supplied by a battery as a function of time is I(t) = Ioe i/T where Io =4.68 A and T =22.7s. Determine the total number of electrons transported from the positive electrode to the negative electrode from the time the battery is first used until it is essentially dead (t = ∞0). (in E electrons, where E = Exa = 1018) I want show all work look at correct answer
College Physics
11th Edition
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Author:Raymond A. Serway, Chris Vuille
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Chapter1: Units, Trigonometry. And Vectors
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The current supplied by a battery as a function of time is I(t) = Ioe i/T
where
Io =4.68 A and T =22.7s. Determine the total number of electrons transported from the positive electrode to the negative electrode from the time the battery is first used until it is essentially dead (t = ∞0). (in E
electrons, where E = Exa = 1018)
I want show all work look at correct answer
![**Title: Calculating the Total Number of Electrons Supplied by a Battery**
**Introduction:**
This exercise involves determining the total number of electrons transported by a battery as it discharges over time. The problem provides a mathematical model for the current supplied by the battery, expressed as a function of time.
**Problem Statement:**
The current supplied by a battery as a function of time is given by:
\[ I(t) = I_0 e^{-t/\tau} \]
where:
- \( I_0 = 4.68 \, \text{A} \) (initial current),
- \( \tau = 22.7 \, \text{s} \) (time constant).
The task is to determine the total number of electrons transported from the positive electrode to the negative electrode from the time the battery is first used until it is essentially dead (\( t = \infty \)).
- The result should be expressed in terms of \( E \) electrons, where \( E = \text{Exa} = 10^{18} \).
**Your Response:**
You answered: 66.397
**Correct Answer:**
The correct answer is: 663.1461 with a margin of error of +/-1%.
**Explanation and Approach:**
To solve this, one would typically integrate the current function over time from \( t = 0 \) to \( t = \infty \) to find the total charge (\( Q \)) in coulombs. Since one coulomb corresponds to approximately \( 6.242 \times 10^{18} \) electrons, converting the total charge into the number of electrons involves dividing by the charge of a single electron.
This problem requires applying knowledge of exponential decay functions, integration, and unit conversions in the context of electric charge and electron flow.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fee22cf2f-b974-4b00-a3cf-09b388e7d65d%2F965941d7-5dc2-4988-97ae-e515a8f86f89%2Ffa0ekka_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Title: Calculating the Total Number of Electrons Supplied by a Battery**
**Introduction:**
This exercise involves determining the total number of electrons transported by a battery as it discharges over time. The problem provides a mathematical model for the current supplied by the battery, expressed as a function of time.
**Problem Statement:**
The current supplied by a battery as a function of time is given by:
\[ I(t) = I_0 e^{-t/\tau} \]
where:
- \( I_0 = 4.68 \, \text{A} \) (initial current),
- \( \tau = 22.7 \, \text{s} \) (time constant).
The task is to determine the total number of electrons transported from the positive electrode to the negative electrode from the time the battery is first used until it is essentially dead (\( t = \infty \)).
- The result should be expressed in terms of \( E \) electrons, where \( E = \text{Exa} = 10^{18} \).
**Your Response:**
You answered: 66.397
**Correct Answer:**
The correct answer is: 663.1461 with a margin of error of +/-1%.
**Explanation and Approach:**
To solve this, one would typically integrate the current function over time from \( t = 0 \) to \( t = \infty \) to find the total charge (\( Q \)) in coulombs. Since one coulomb corresponds to approximately \( 6.242 \times 10^{18} \) electrons, converting the total charge into the number of electrons involves dividing by the charge of a single electron.
This problem requires applying knowledge of exponential decay functions, integration, and unit conversions in the context of electric charge and electron flow.
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