In the LCR circuit the ac driving voltage is v = vm sin ωt.
(i) Write down the equation of motion for q (t).
(ii) At t = t0, the voltage source stops and R is short-circuited. Now write down how much energy is stored in each of L and C.
(iii) Describe subsequent motion of charges.
(i) The equation for variation of motion of charge with respect to time is given as
L d2q(t)/dt + R dq(t)/dt + q(t)/C = Vm sin ωt
(ii) The energy stored in each of L and C is given as
Uc = 1/2Cω2[Vm2/R2+(XC – Xl)2] cos2 (ωto + ϕ)
(iii) For the circuit to become LC oscillator, R needs to be short-circuited. By doing so, the capacitor will continue to discharge and all the energy will be transferred to L and back and forth. This way there will be an oscillation of energy from electrostatic to magnetic.