- #1
vorcil
- 398
- 0
I wanted to see the proof for the energy stored in an inductor equation was,
But i had trouble understand how part of this integration works i.e my math sucks
-
given [tex] \frac{dw}{dt} = iv [/tex]
and [tex] VL = L \frac{di}{dt} [/tex]
-
solving i get,
subtituting the ldt/dt for v
[tex] \frac{dw}{dt} = i L \frac{di}{dt} [/tex]
the dt's cancel out
[tex] dw = i L di [/tex]
then to find the work done I integrate the equation,
[tex] \int dw = \int i L di [/tex]
and the integral of [tex] \int dw = w [/tex]
but how do I integrate
[tex] \int i L di [/tex] ?
I know L, the inductance of the inductor is constant so can pull that outside the integral,
and get
[tex] L \int i di [/tex]
But what do I do here?
integrating i I get [tex] \frac{1}{2} i ^2 * i [/tex] according to the integration rules I've learnt
but everyone knows that the energy inside an inductor equation is
[tex] wL = \frac{1}{2} L i^2, [/tex]
but my integration shows it is [tex] \frac{1}{2} L i^3 [/tex]
can someone please explain it to me
But i had trouble understand how part of this integration works i.e my math sucks
-
given [tex] \frac{dw}{dt} = iv [/tex]
and [tex] VL = L \frac{di}{dt} [/tex]
-
solving i get,
subtituting the ldt/dt for v
[tex] \frac{dw}{dt} = i L \frac{di}{dt} [/tex]
the dt's cancel out
[tex] dw = i L di [/tex]
then to find the work done I integrate the equation,
[tex] \int dw = \int i L di [/tex]
and the integral of [tex] \int dw = w [/tex]
but how do I integrate
[tex] \int i L di [/tex] ?
I know L, the inductance of the inductor is constant so can pull that outside the integral,
and get
[tex] L \int i di [/tex]
But what do I do here?
integrating i I get [tex] \frac{1}{2} i ^2 * i [/tex] according to the integration rules I've learnt
but everyone knows that the energy inside an inductor equation is
[tex] wL = \frac{1}{2} L i^2, [/tex]
but my integration shows it is [tex] \frac{1}{2} L i^3 [/tex]
can someone please explain it to me