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

**Strings (S _{i}P_{j}A_{jk}) = S_{7}P_{4}A_{41} Base Sequence = 12735 String Sequence = 12735 - 4 - 41 **

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

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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) S_{7}P_{4}A_{41} (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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