In my Nilsson "Electric Circuits, 5th ed" book, there's this drill exercise near the beginning of the book.

Here it is:

Current at the terminals of the element is

t<0: $$ i=0 $$ t>=0: $$ i=10e^{-2000t} Amps $$

Calculate the total charge in microC entering the element at its upper terminal

The element is just an ideal basic circuit element with two terminals.

The answer is 5000 microcoulombs.

This is very early on in the book, in a chapter describing Voltage and Current.

With current as i = dq/dt

I have no idea how to go about it, since the book said algebra would be used until capacitors and inductors, and that no problem-solving tools were given for it.

Is it some calculus-related question? I tried putting in the values in the

i = dq/dt

but my calculator said "calculation error". (from the -2000 exponent, probably)

Any help would be appreciated, thank you for your time. :)


Yes, it is a calculus question. To undo the derivative, you need to take an integral. This can be done by hand, or using an online tool like Wolfram Alpha:

\$\int_0^{\infty} 10 e^{-2000 t} \text{A} dt = 0.005 \;\text{A}\cdot\text{s} = 5000 \;\text{µC}\$

  • \$\begingroup\$ How does one know if it's 0 to infinity in the integral? \$\endgroup\$ – user27810 Aug 21 '13 at 14:44
  • 1
    \$\begingroup\$ Before t=0, there's no current flow, so times before that don't matter. It's an exponential decay, which never actually reaches zero, so you have to integrate over all time from t=0 on. \$\endgroup\$ – Stephen Collings Aug 21 '13 at 14:49
  • \$\begingroup\$ Nicely put answer \$\endgroup\$ – Andy aka Aug 21 '13 at 16:20

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