How to determine number of electrons?

Question

The net charge through a cross section of a circuit element is given by q(t) = 2 + 3t. The current through the element is 3 Amps. How many electrons pass this cross section in 2 seconds?

Answer 1

An amp (A) is defined as the amount of charge (in coulombs or C) transferred past a given point in 1 second.

1A = 1C / 1sec

Current (amps) is defined as the rate of change of charge (coulombs) over time:

i(t) = dq/dt

i(t) = d/dt (2 + 3t) = 3 Amps (as you said in your question)

so multiplying that first equation by 3 we get:

3A = 3C/sec

but the time interval we are given is 2 sec (not 1 second), so we will multiply the number of coulombs by 2 and find the total charge to be 6C.

1C (coulomb) is the amount of electrical charge in 6.241506×10^18 electrons.

So 6 coulombs contain 6×(6.241506×10^18) electrons

or 37.449036×10^18 electrons

also can be written as 3.7449036×10^19 electrons