Question

An oscillating LC circuit consists of a 75 mH inductor and a 1.2 uF capacitor. If the maximum charge to the capacitor is 2.7μC. The maximum current in the circuit will be _____mA.

Hint:

Energy conservation in LC circuits ensures smooth oscillations between capacitor and inductor.

Answer 1

Correct Answer: 9

Step 1: Use the energy conservation in LC circuits - Maximum energy in capacitor = Maximum energy in inductor: \[ \frac{1}{2} L I_{\text{max}}^2 = \frac{1}{2} \frac{q_{\text{max}}^2}{C}. \]

Step 2: Solve for \(I_{\text{max}}\) - \[ I_{\text{max}} = \frac{q_{\text{max}}}{\sqrt{L C}}. \] Substituting values: \[ I_{\text{max}} = \frac{\sqrt{2.7 \times 10^{-6}}}{\sqrt{75 \times 10^{-3} \cdot 1.2 \times 10^{-6}}}. \] Simplifying: \[ I_{\text{max}} = 9 \times 10^{-3} \, \text{A} = 9 \, \text{mA}. \]

Final Answer: The maximum current in the circuit is 9 mA.