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.