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Show that the charges oscillate with a frequency given byomega = (1)/( sqrt(LC))when a charged capacitor of capacitance C is connected to an inductor of inductance L. |
Answer» Solution : Consider a capacitor of capacitance C. Let it be CHARGED `q_0` and connected to an ideal inductor of inductance L as shown in fig. The capacitor begins to discharge. As it does so an emf is induced in the inductor. At any instant p.d. across the capacitor = p.d. across the inductor. `(q)/(C ) =-L(dI)/( dt)` `(q)/(C ) +l (DL)/(dt)=0` Where, q and I are the charge and current at any instant But ` I=(dI)/(dt)to (2)` `therefore(q)/(C )+L ((d)/(d t)) ((dq)/( dt)) =0` ` ((d^2 q)/(dt^2))+(q)/(LC) =0TO (3)` The above relation is in the FORM of ` (d^2x)/( dt^2)+ omega ^2x=0to (4)` On comparing (3) and (4) we GET `omega^2= (1)/(LC)` ` omega=(1)/(sqrt(LC))` |
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