Question

Define one coulomb charge.

Answer 1

Hint : The rate of change of charge flowing through a point with time is the current. The smallest unit of charge is the magnitude of charge of a proton or the charge of an electron, which is equal to $1.6 \times {10^{ - 19}}C$

Formula used: In this solution we will be using the following formula;
$I = \dfrac{{dq}}{{dt}}$ where $I$ is the current flowing through a point, $q$ is the charge passing through that point and $t$ is the time for a particular amount of charge to flow.
$\dfrac{{dq}}{{dt}}$ signifies an instantaneous rate of the charge with time.

Complete step by step answer
The current flowing through a point in space is the time rate at which charges pass through that point.
This is mathematically given as
$I = \dfrac{{dq}}{{dt}}$ where $I$ is the current flowing through a point, $q$ is the charge passing through that point and $t$ is the time for a particular amount of charge to flow. $\dfrac{{dq}}{{dt}}$ signifies an instantaneous rate of the charge with time.
Hence, the charge can be given as
$dq = Idt$
By integration, we have that
$q = \int {dq} = \int {Idt}$
If the current is constant, we can write
$q = It$
Now, the unit of charge is the coulomb, the unit of current is the Ampere and the unit of time is seconds.
Hence, we can define a coulomb of charge to be the amount of charge passing through a point when a constant current of 1 Ampere is flowing for exactly 1 second.

Note
Alternatively, since the smallest unit of charge is the charge on a proton which is given as $1.6 \times {10^{ - 19}}C$ .
Hence we have $1.6 \times {10^{ - 19}}\dfrac{C}{{proton}}$ . Then by inverting we would have
$\dfrac{1}{{1.6 \times {{10}^{ - 19}}}}\dfrac{{proton}}{C} = 6.25 \times {10^{18}}\dfrac{{proton}}{C}$
Hence, the one coulomb charge can be defined as the amount of charge possessed by $6.25 \times {10^{18}}$ protons.