﻿ Electric Current: Charge Passing Through A Fixed Point Per Unit Time

Electric Current: Charge Passing Through A Fixed Point Per Unit Time

Strings (SiPjAjk) = S7P4A41     Base Sequence = 12735     String Sequence = 12735 - 4 - 41

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Expressions Of Pj Problems
Electric Current: Charge Passing Through A Fixed Point Per Unit Time
Math

The coulomb of charge, q, moving pass a fixed point on a conductor in time t, is given by the time-variable function:
q(t) = (4x10-4)(1 - e-250t) Coulombs -----------(1)
Determine the current passing through the fixed point at time, t = 3 ms (milliseconds).

The string:
(a) S7P4A41 (Linear Motion - Current).
The math:
Pj Problem of Interest is of type motion. It could also be viewed as of type change because current is the rate of change of charge flow with respect to time. However, its representation as the flow of charge is more appropriate perspectively.
For a time-variable flow of charge, current is the derivative of the charge function, q(t).
So, the current, i = dq/dt.
So, dq/dt = (4x10-4)(250e-250t)----(2).
Substituting t = 3 ms = 3 x 10-3 s, into (2):
So, dq/dt = (4x10-4)(250e-250x3 x 10-3)
= .0004 x 250 x .4730 = .0473 Amperes = 47.3 mA
So, Current passing through fixed point = 47.3 mA.

The point . is a mathematical abstraction. It has negligible size and a great sense of position. Consequently, it is front and center in abstract existential reasoning.
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