A capacitor C charged to voltage V is discharged into an inductor L. What is the voltage on C at the instant when its stored energy and inductor's energy are equal?
Short answer: energy in capacitor goes as square of voltage across it, and since there are not dissipative losses (ideal inductor and capacitor), there will be half the energy in the capacitor and therefore equal energy in the inductor when the capacitor voltage is V / sqrt(2) Long answer: Energy in inductor is (1/2)Li^2, energy in capacitor is (1/2)Cv^2, and i C dv/dt, so energy in both components is the same when L i^2 L C^2 (dv/dt)^2 C v^2 LC (dv/dt)^2 v^2 But we also know that the voltage as a function of time will be v V cos( t / sqrt(LC) ) dv/dt -V / sqrt(LC) sin( t / sqrt(LC) ) Substitute this expression for dv/dt into above energy balance to get LC (V^2 / LC) sin^2( t / sqrt(LC) ) V^2 cos^2( t / sqrt(LC) ) sin( t / sqrt(LC) ) +/- cos( t / sqrt(LC) ) The first point of equality is when t (Pi/4)sqrt(LC), and substituting that into expression for v gives: v V cos(Pi/4) V / sqrt(2)
energy stored in charged capacitor is 1/2(c*v^2) and energy stored in inductor is given by 1/2(l*i^2).so when the energies are equal then vsquareroot(l*i/c)
