Electrical Engineering question.?

Question

The voltage and current for an unidentified circuit element w/ 2 terminals are zero for t < 0. For t >/= 0 they are
v = 50 e^(-1600t) - 50 e^(-400t) Volts
i = 5 e^(-1600t) - 5 e^(-400t) Amps
How much energy is delivered to the circuit element between 0 and 625 microseconds?
Note: Current is flowing in the direction of a voltage drop.

Note that I'm to find the total energy over a specified period of time. I think I need to integrate over the interval 0 to 625 microseconds, but I tried that and I can't seem to get it right.

Answer 1

by factoring we need to integrate
[e^(-1600t) - e^(-400t)]^2 dt
and multiply the result by 250

Next we integrate

e^(-3200t) - 2 e^(-2000t) + e^(-800t)

this yields

-e^(-3200t)/3200 + e^(-2000t)/1 000 - e^(-800t)/800

at 625uS this is
-4.2292e-5 + 2.86505e-4 - 7.58163 e-4
= -5.1395 e-4

at 0 it is
-5.625 e-4
the difference is
4.855 e-5

multiplying by 250
12.1mJ

Answer 2

I'm a retired electrician with over 35 years experience and a good technical background. With no identifiable circuit background the question assumes no characteristitics of time.So, standard equations apply, Electrical products are instantaneous once the circuit is made. Either you or your professor is an idiot. And current always flows in the direction of a voltage drop.

Answer 3

Total energy is the integral of power over time. Power in an electrical circuit is voltage times current. The formula is then ∫[0-625µsec] v*i dt You have the functions for v and i, then do the integration. Watch your units: v (volts) * i (amps) = W (watts). ∫Wdt = joules = watt*sec