Question

A conductor carries a current of $0.2Amp$. In $30s$ how many electrons will flow through the cross section of the conductor, take $q = 1.6 \times {10^{ - 19}}C$
a. $0.375 \times {10^{ - 19}}$
b. $375 \times {10^{ - 19}}$
c. $3.75 \times {10^{ - 19}}$
d. $37.5 \times {10^{ - 19}}$

Answer 1

Hint: In the question they have asked us to find the charge of a conductor, the flow of electrons is nothing but the current or charge. To calculate the total charge, we have to use the value for the charge of one electron.

Formula used:
To measure the charge:
$Q = I \times t$
Where,
$Q$is the charge
$I$is the current
$t$is time for the flow of electrons.
To calculate the total charge:
$Q = n.q$
Where,
$n$is the number of flow of electrons
$q$is the charge of one electron.

Complete step by step answer:
In the question, it is given that a conductor carries a current of $0.2Amp$. We have the time of flow of electrons that is $30s$. First we can calculate the value of charge that is $Q$.
We can find the value of charge by multiplying the current value and time taken by the electrons to flow. That is,
$ \Rightarrow Q = I \times t$
Where,
$Q$ is the charge
$I$ is the current
$t$ is time for the flow of electrons.
We have the values. Now we can substitute the values in the formula.
$ \Rightarrow Q = 0.2 \times 30$
 On multiplying we get the value of charge. That is,
$ \Rightarrow Q = 6C$
We have now found the value for the charge. In the question they have asked us to find how many electrons that flow.

We know that the total charge is calculated by multiplying the values of the number of electrons and the charge of one electron. We can represent this in a formula. That is,
$ \Rightarrow Q = n.q$
Where,
$n$ is the number of flow of electrons
$q$ is the charge of one electron

To find the number of electrons we can divide the total charge of electrons and the charge of one electron. That is,
$ \Rightarrow n = \dfrac{Q}{q}$
We have the values of $Q = 6C$ and $q = 1.6 \times {10^{ - 19}}C$, on substituting we get,
$ \Rightarrow n = \dfrac{{6C}}{{1.6 \times {{10}^{ - 19}}C}}$
We can use division for the simplifications we get,
$ \Rightarrow n = 3.75 \times {10^{ - 19}}$
$\therefore n = 3.75 \times {10^{ - 19}}$ is the number of electrons that flow through the cross section of the conductor in $30s$.

Hence, the correct answer is option (C).

Note: The flow of charges is called as current. There are two types of current known as alternating current and direct current. If the current that flows in one direction is known as Direct current and the flow of current in alternate directions is known as Alternating current. D.C is the current primary source for industries and A.C is for household works.