In a circuit shown in figure the battery emf is equal to `E=2.0 V`, its internal resistance is `r=9.0 Omega`, the capacitance of the capacitor is `C=10 mu F`, the coil inductance is `L=100 m H`, and the resistance is `R=100 Omega` . At a certain momenta the switch `Sw` was disconneted.
Find the energy of oscillations in the circuit
(b) `t=0.30s` after the switch was disconnected,

Explanation

At `t=0` current throught the coil `=(epsilon)/( R+r)`
`P.D.` across the condenser `=(epsilon)/( R+r)`
`(a) ` At `t=0`, energy stroed` =W_(0)`
`=(1)/(2) L((epsilon)/R+r)^(2)+(1)/(2)C((epsilon)/( R+r))^(2)=(1)/(2)epsilon^(2)((L+CR^(2)))/((R+r))=20mJ`
`(b)` The current and the change stores decrease as `e^(-tR//2L)` so energy decreases as `e^(-tR//L)`
`:. W=W_(0)e^(-tR//L)=0.10mJ.`