An LC circuit is formed by connecting an unknown capacitor to an inductor of inductance 20 mH . The capacitor was initially charged to a potential difference of 50 V . If the maximum current in the circuit during the LC oscillations is 2 A , the capacitance of the capacitor is _____ F .

Step-by-step solution

By the principle of conservation of energy in an LC circuit, the maximum electrical energy stored in the capacitor is equal to the maximum magnetic energy stored in the inductor. 1 2 CV₀^2 = 1 2 LI_ max ^2 Given: V₀ = 50 V L = 20 mH = 20 10⁻³ H I_ max = 2 A Substituting the values: C(50)^2 = (20 10⁻³)(2)^2 2500 C = 80 10⁻³ C = 80 10⁻³ 2500 = 32 10⁻⁶ F Thus, the capacitance is 32 F . Answer: 32