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)

• A. \(\frac{Q_{0}}{\sqrt{2}}\)
• B. \(\frac{Q_{0}}{2}\)
• C. \(\sqrt{2}Q_{0}\)
• D. \(Q_{0}\)

Hint:

The total energy in an ideal LC circuit stays constant. If the two energies are equal, the capacitor holds half the total.

Answer 1

The Correct Option is A

Step 1: Energy balance
Total energy $=U_{C}+U_{L}=2U_{C}$ when the two are equal.

Step 2: Relate to the charge
$2\cdot\dfrac{Q^{2}}{2C}=\dfrac{Q_{0}^{2}}{2C}$

Step 3: Solve
$Q^{2}=\dfrac{Q_{0}^{2}}{2}$, so $Q=\dfrac{Q_{0}}{\sqrt{2}}$, option (A). Option (B) would be correct only if the charge, not the energy, were halved.

Final Answer:
The charge is Q0 over root 2. \[ \boxed{\text{(A) }\dfrac{Q_{0}}{\sqrt{2}}} \]