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A copper wire of cross-sectional area $2.0\;mm^2$ carries a current of $10\;A$. How many electrons pass through a given cross-section of the wire in one second?

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Last updated date: 29th Feb 2024
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IVSAT 2024
Answer
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Hint: We know that only conductors like metals copper allow the flow of electric current via them. To begin with we can define what is electric current to find the required answer. Also note that to solve this problem, we don’t need the cross-sectional area of the copper wire.
Formula used:
$I=\dfrac{Q}{t}$

Complete answer:
From the definition of current, we know that current is flow of charges per unit time. Since electrons are free to move around in a conductor, we can say that current is the flow of electrons per unit time. Also the SI unit of current is ampere A. Generally current is measured using a device called ammeter.

Complete answer:
Clearly, one ampere is the flow of one coulomb of charges i.e electrons across a surface in unit second. And is mathematically written as $I=\dfrac{Q}{t}$.
Also , we know that one coulomb is $6.24\times 10^{18} electrons$ , which can be represented as$1 C= 6.24 \times 10^{18} electrons$
Then, from the definition of current and coulomb, we have, $1 A=6.24\times 10^{18} electrons /sec$
Here, we have to find the electrons due to $10\; A$ then, we have
$\implies 10A=10\times 6.24 \times 10^{18} electrons / sec$
$\therefore 10A=62.4 \times 10^{18} electrons/sec$
Thus we can say that there are$62.4 \times 10^{18} electrons / sec$ which flow via conductor carrying $10\;A$ current.

Note:
Coulomb is nothing but the electric charge carried by one ampere current per one second via a current carrying conductor. It was found by various experiments that $1 C= 6.24 \times 10^{18} electrons$. Thus from the definition of the current and coulomb, we can solve the following. Also note that the terms coulomb are current are interdependent and one is used to define the other. However, there is a little additional information given in the question which can be avoided.
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