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  • A fully charged capacitor C with initial charge  is connected to a coil of self inductance L

A fully charged capacitor C with initial charge \mathrm{q}_0 is connected to a coil of self inductance L at t = 0. The time at which the energy is stored equally between the electric and the magnetic field is:

Option: 1

\frac{\pi}{4} \sqrt{\mathrm{LC}}


Option: 2

2 \pi \sqrt{\mathrm{LC}}


Option: 3

\sqrt{\mathrm{LC}}


Option: 4

\pi \sqrt{\mathrm{LC}}


Answers (1)

best_answer

As \mathrm{\omega^2=\frac{1}{\mathrm{LC}} or \omega=\frac{1}{\sqrt{\mathrm{LC}}} }
Maximum energy stored in capacitor =\mathrm{\frac{1}{2} \frac{Q_0^2}{C} }
Let at an instant t, the energy by stored equally between electric and magnetic field. The energy stored in electric field at instant \mathrm{\mathrm{t} } is
\mathrm{\frac{1}{2} \frac{\mathrm{Q}^2}{\mathrm{C}}=\left[\frac{1}{2} \frac{\mathrm{Q}_0^2}{\mathrm{C}}\right] }
or \mathrm{\quad \mathrm{Q}^2=\frac{\mathrm{Q}_0^2}{2} \quad or \quad \mathrm{Q}=\frac{\mathrm{Q}_0}{\sqrt{2}} \quad or \quad \cos \omega } 
\mathrm{\mathrm{t}=\frac{\mathrm{Q}_0}{\sqrt{2}} }
or \mathrm{\quad \omega \mathrm{t}=\frac{\pi}{4} \quad or \quad \mathrm{t}=\frac{\pi}{4 \omega}=\frac{\pi}{4 \times(1 / \sqrt{\mathrm{LC}})}=\frac{\pi \sqrt{\mathrm{LC}}}{4} }

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