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(D) When the switch is in position $a$,the capacitor is charged to a potential $E$. The charge on the capacitor is $q = CE$.The energy stored in the c

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$E \sqrt{C/L}$

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(D) When the switch is in position $a$,the capacitor is charged to a potential $E$. The charge on the capacitor is $q = CE$.The energy stored in the capacitor is $U = \frac{q^2}{2C} = \frac{(CE)^2}{2C} = \frac{1}{2} CE^2$.When the switch is thrown to position $b$,the circuit becomes an $LC$ oscillator. The total energy is conserved,oscillating between the electric field of the capacitor and the magnetic field of the inductor.Let $I_0$ be the amplitude of the oscillating current. The maximum magnetic energy in the inductor is $\frac{1}{2} L I_0^2$.By the law of conservation of energy,the maximum electrical energy equals the maximum magnetic energy:$\frac{1}{2} CE^2 = \frac{1}{2} L I_0^2$$CE^2 = L I_0^2$$I_0^2 = \frac{C}{L} E^2$$I_0 = E \sqrt{\frac{C}{L}}$

In the circuit shown below,the switch is kept in position $a$ for a long time and is then thrown to position $b$. The amplitude of the resulting oscillating current is given by

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