Question

The equation of the currentin a pure inductor circuit is i =4.25 sin 157t when the impressed emfwave is e = 650 cos 157t. Determine the equation of the powerwave and operating frequency.

Answer 1

not familiar with the term "powerwave" as such

for the power isn't it volts times amps equals watts ?

as a starting approx, i'd go for 650(volts?)x4.25(amps?)=2762.5 about 3kilo watts. Looks like heavy duty stuff this.

possibly some messing about with RMS involved.

hmmmm ..... LOOKS like the op freq is contained in the 157 term.
that looks like omega, which looks like 2 pi f.
2 pi f = 157
f = 25Hz

the 3kW estimate and the 25Hz estimate suggest to me that this is a problem from heavy duty electrical engineering. Perhaps an electric fire or a furnace of some sort ?

i think (sometimes .... if I absolutely have to)

Answer 2

" i =4.25 sin 157t when the impressed emfwave is e = 650 cos 157t. Determine the equation of the powerwave"


\(p = i \cdot e = 4.25 \sin 157t \cdot 650 \cos 157t \)

with the double angle identity...
\(= \frac{1}{2} 4.25 \cdot 650 \sin (2 \cdot 157t)\)

.... and continue to simplify

there may be a minus sign in there as the L creates a back voltage. (if you need that level of detail as opposed to just the numbers)


"and operating frequency"

what does that mean. you have the input frequency - see @osprey's post - but also a doubled freq in terms of power. is that what you mean?

oc, use \(\omega = 2 \pi f\) to extract the f

Answer 3

thanks