An LC circuit consists of an inductor of inductance L and a capacitor of capacitance C . At time t = 0 , the capacitor has a charge Q 0 and the current in the inductor is I 0 . Match the quantitie

Question

An LC circuit consists of an inductor of inductance $L$ and a capacitor of capacitance $C$ . At time $t = 0$ , the capacitor has a charge $Q_{0}$ and the current in the inductor is $I_{0}$ . Match the quantities in List-I with their corresponding expressions in List-II.

List - I	List - II
(P) Maximum charge on the capacitor	(1) $\frac{1}{L C}$
(Q) Maximum current in the inductor	(2) $Q_{0}^{2} + L I_{0}^{2} C$
(R) Total energy stored in the circuit	(3) $\frac{Q _{0}^{2}}{2 C} + \frac{1}{2} L I_{0}^{2}$
(S) Angular frequency of oscillation	(4) $I_{0}^{2} + \frac{Q _{0}^{2}}{L C}$

TestHub · Accepted Answer

The total energy in the LC circuit is E = 2 C Q 0 2 ​ ​ + 2 1 ​ L I 0 2 ​ . At maximum charge Q ma x ​ , E = 2 C Q ma x 2 ​ ​ , so Q ma x ​ = Q 0 2 ​ + L I 0 2 ​ C ​ . At maximum current I ma x ​ , E = 2 1 ​ L I ma x 2 ​ , so I ma x ​ = I 0 2 ​ + L C Q 0 2 ​ ​ ​ . The angular frequency of oscillation is ω = L C ​ 1 ​ .

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