A 4 ~F capacitor is charged to 10 V . The battery is then disconnected and a pure 10 mH coil is connected across the capacitor so that LC oscillations are set up. The maximum current in the coil is

Step-by-step solution

In an LC circuit, energy conservation requires that the maximum current occurs when all initial capacitor energy transfers to the inductor. The initial energy stored in the capacitor is U_C = 1 2 CV^2 = 1 2 (4 10⁻⁶ F )(10 V )^2 = 2 10⁻⁴ J . When the current reaches its maximum I_ max , the inductor energy equals the initial capacitor energy: 1 2 LI_ max ^2 = 1 2 CV^2 . Solving for I_ max yields I_ max = V C L . Substituting L = 10 mH = 10⁻² H gives I_ max = 10 V 4 10⁻⁶ F 10⁻² H = 10 4 10⁻⁴ = 10 0.02 = 0.2 A . Final