Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Energy in inductor and capacitor

  1. Aug 21, 2010 #1
    Energy in inductor is given as (Li2])/2
    but energy is power absorbed in t secs is E=integral(from 0 to t)Lidi here i is current.
    since this integral stretches from 0 to t After doing the integral the current i must be turned into the time variable i.e E=(Lt2)/2;
    Then why are we writing it as i2 what is this i represent. Is this the current i and this Energy i the same or different.

    Same problem for capacitance in terms of voltage
    Last edited: Aug 21, 2010
  2. jcsd
  3. Aug 21, 2010 #2
    Power,P=Ei where E stands for the emf due to the inductive effect
    Energy spent in time [0 to t]= integral[0 to t]Eidt

    |E|= L di/dt

    Energy expended= integral[0 to t]Li di/dt * dt
    = integral[0 to i]Li di [please do note the change of variable here]
    = 1/2 Li^2
  4. Aug 21, 2010 #3
    since they may not be equal how could time change into current.
    Let us suppose we want to find energy for 2 secs with current of x amps , and inductance 1 henry , then
    IS E=0.5x joules using i as variable in boundary value correct or E=2 joules using t as variable in boundary value is a correct one.
    Last edited: Aug 21, 2010
  5. Aug 21, 2010 #4
    Things would become clear if you know how current is changing with time i=i(t)

    if you know the above function you can again find f(t) =di/dt
    Then you find:

    integral[0 to 2]L*i(t)* f(t)dt ------------- (1)

    You use the relation i=i(t) to calculate the current at time=2 seconds
    that is you find i(2),noting i(0)=0

    Energy expended=
    = integral[0 to i(2)]Li di
    = 1/2 Li(2)^2 ---------------- (2)

    (1) and (2) should give you the same result for any function i=i(t)provided they are differentiable and provided i(0)=0
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook