Question

How many electrons constitute a current of one microampere?
A. $6.25 \times {10^6}$
B. $6.25 \times {10^{12}}$
C. $6.25 \times {10^9}$
D. $6.25 \times {10^{15}}$

Answer 1

Hint: Start by using the definition of current , which is defined as the amount of charge flowing through the conductor per unit time. Substitute all the values of given physical quantities and find out the number of electrons present in 1 microampere of current.

Complete answer:
We know 1 Ampere is defined as the amount of charge flowing through the conductor in 1 second.
And the formula for current is given by the relation $I = \dfrac{q}{t}$, where q is the amount of charge , t is the time taken for the flow.
We know $q = ne$, where n is the number of charge particles and e is the amount of charge on an electron.($1.6 \times {10^{ - 19}}C$)
Here $I = 1\mu A,t = 1\operatorname{s} $, we know $1\mu A = {10^{ - 6}}A$
$
  I = \dfrac{{ne}}{t} \\
   \Rightarrow n = \dfrac{{It}}{e} \\
$
Substituting the values in the above equation , we get
$n = \dfrac{{1 \times 1}}{{1.6 \times {{10}^{ - 19}}}} = 6.25 \times {10^{12}}$
Therefore, number of electron = $6.25 \times {10^{12}}$

So, the correct answer is “Option B”.

Note:
Alternative solution
We know ,1 coulomb = $6.242 \times {10^{19}}$ electrons
Also, “1 ampere” is equal to “1 coulomb per second”,
1 ampere = $6.242 \times {10^{18}}$ electrons/sec
1 ampere = 1000 milliampere
And 1 milliampere =1000 microampere
Therefore, 1 ampere = $6.242 \times {10^{12}}$ electrons
Such similar questions can also be asked for 1v of potential difference or $1\mu F$ of capacitance, and can be solved by using relevant formulas related to the quantities and its definition. One must be well thorough with the definitions and formulas of such important physical quantities. Attention must be given while converting the units, as most of the students make mistake here itself