Question

A current of 4.8 A is flowing in a conductor. The number of electrons passing per second through the conductor will be:
A. \[3 \times {10^{20}}\]
B. \[76.8 \times {10^{20}}\]
C. \[7.68 \times {10^{ - 19}}\]
D. \[3 \times {10^{19}}\]

Answer 1

Hint: Electric current is set up when the charges are flowing in a conductor. How much current is flowing in the conductor can be determined by how much the charge is flowing with respect to the time taken. Also by quantization of charge, charges can transfer in the form of fixed amounts. So charge always exists in the integral multiple of minimum charge that is e. 

Formula used
By quantization of charge,
\[q = ne\]
Where q is charge, n is an integer or number of electrons and e is charge on each electron.
As current is defined as the rate of flow of charge.
\[I = \dfrac{q}{t}\]
Where $I$ is the current, q is in charge and t is time taken.

Complete step by step solution:
Given Current flowing in conductor, \[I = 4.8A\]
Let the number of electrons passing per second through the conductor be n.
Charge of each electron = \[1.6 \times {10^{ - 19}}C\].......(Unit of charge is Coulomb and represented as C)

As we know the current is defined as the rate of flow of charge in a conductor.
\[I = \dfrac{q}{t}\]
As \[q = ne\]
Putting this in above equation, we get;
\[I = \dfrac{{n \times e}}{t}\]
Or can be written as,
\[\dfrac{n}{t} = \dfrac{I}{e}\]

Substituting the given values,
\[\dfrac{n}{t} = \dfrac{{4.8}}{{1.6 \times {{10}^{ - 19}}}}\]
\[\Rightarrow \dfrac{n}{t} = 3 \times {10^{19}}\]
\[\therefore n = 3 \times {10^{19}}{\text{ electrons per second}}\]
Therefore, the number of electrons passing per second through the conductor is \[3 \times {10^{19}}\].

Hence option D is the correct answer.

Note: When the charges are at rest, then its study is under electrostatics which studies the charges at rest. When the charges start moving, then its study is under dynamics which studies the moving charges. Due to the flow of charges, an electric current is produced. Since e is the smallest value of charge so it is called an elementary charge or fundamental charge. A charge is a measure of total current that flows within a period of time.