An oscillating LC circuit consists of a 75 mH inductor and a 1.2 $$\mu$$F capacitor. If the maximum charge to the capacitor is 2.7 $$\mu$$C. The maximum current in the circuit will be ______ mA.

We are given an oscillating LC circuit with inductance $$L = 75$$ mH $$= 75 \times 10^{-3}$$ H, capacitance $$C = 1.2$$ $$\mu$$F $$= 1.2 \times 10^{-6}$$ F, and maximum charge $$Q_0 = 2.7$$ $$\mu$$C $$= 2.7 \times 10^{-6}$$ C.

Apply energy conservation. At maximum charge, all energy is in the capacitor. At maximum current, all energy is in the inductor:

$$ \frac{Q_0^2}{2C} = \frac{LI_0^2}{2} $$

Solve for maximum current: $$ I_0 = \frac{Q_0}{\sqrt{LC}} $$

Calculate $$\sqrt{LC}$$: $$ LC = 75 \times 10^{-3} \times 1.2 \times 10^{-6} = 90 \times 10^{-9} = 9 \times 10^{-8} $$

$$ \sqrt{LC} = \sqrt{9 \times 10^{-8}} = 3 \times 10^{-4} \text{ s} $$

Find $$I_0$$: $$ I_0 = \frac{2.7 \times 10^{-6}}{3 \times 10^{-4}} = 0.9 \times 10^{-2} = 9 \times 10^{-3} \text{ A} = 9 \text{ mA} $$

The maximum current in the circuit is 9 mA.