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Physics

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A circuit contains a self-inductance L in series with a capacitor C and a resistor R. This circuit is driven by an alternating voltage V=V0sin(ωt). We have L=0.015 H, R= 80 Ω, C= 5e-06 F, and V0=40 volts.

Q) Find the energy UC(t) and the energy UL(t) stored in the capacitor and in the inductor, respectively, at time t1=0.0003 seconds for ω=ω0. Express your answers in Joules.

UC(t1): ???
UL(t1): ???

  • Physics -

    plz help !

  • Physics -

    V=V₀sinωt,
    ω= ω₀=1/sqrt(LC)=1/sqrt(0.015•5•10⁻⁶)= =3652 rad/s.

    V(t)=40sin3652t.
    q=CU,
    q(t) =CV₀sinωt,
    q(t) =5•10⁻⁶•40sin3652t=2•10⁻⁴sin3652t,
    I(t) =dq/dt =d(CV₀sinωt)/dt= CV₀ωcosωt,
    I(t)= 5•10⁻⁶•40•3652cos3652t =
    =0.73cos3652t.

    UC=CV²/2=CV₀²sin²ωt/2=
    =(5•10⁻⁶•40²/2) sin²3652t=
    =0.004 sin²3652t,

    UC(t₁) = 0.004 sin²(3652•0.0003)=
    =0.0032 J.

    UL =LI²/2 = L(CV₀ω)²cos²ωt/2 =
    =(0.015•(0.73)²/2)cos²3652t = =4•10⁻³cos²3652t,

    UL(t₁) = 4•10⁻³cos²(3652•0.0003)=
    =8.37•10⁻⁴J.

  • Physics -

    am not getting these answers marked correct ! plz if u can check it again ! thnx :)

  • Physics -

    anyone get this

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