In an ideal LC circuit, if the energy stored in the inductor is equal to energy stored in a capacitor, then the magnitude of charge Q stored in capacitor is ( Q 0 is the maximum charge)

Question

In an ideal LC circuit, if the energy stored in the inductor is equal to energy stored in a capacitor, then the magnitude of charge Q stored in capacitor is ( Q 0 ​ is the maximum charge)

TestHub · Accepted Answer

Total energy in an ideal LC circuit is conserved and is equal to the maximum energy stored in the capacitor.

$E_{t o t a l} = \frac{Q _{0}^{2}}{2 C}$

At any instant, the total energy is the sum of the energy stored in the capacitor ( $U_{C}$ ) and the inductor ( $U_{L}$ ).

$E_{t o t a l} = U_{C} + U_{L}$

Given that the energy stored in the inductor is equal to the energy stored in the capacitor ( $U_{L} = U_{C}$ ):

$E_{t o t a l} = 2 U_{C}$

Substituting the expressions for energy:

$\frac{Q _{0}^{2}}{2 C} = 2 (\frac{Q ^{2}}{2 C})$

$Q^{2} = \frac{Q _{0}^{2}}{2}$

$Q = \frac{Q _{0}}{2}$

Answer: $\frac{Q _{0}}{2}$

Physics - Capacitor Question with Solution | TestHub

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