In the LC circuit shown in the figure initial current through the inductor is zero, initial voltage across the capacitor is 100 V. Switch S is closed at t = 0 sec. The current through the circuit is [Figure description: A single series loop containing an inductor L = 20 mH (top), a capacitor C = 1 µF on the right side (initially charged to 100 V, with the minus plate on top and plus plate on the bottom), and a switch S (closing at t = 0) on the left side.]
- A. 7.07 sin (7.07 × 10^3 t)
- B. 0.707 cos (7.07 × 10^3 t)
- C. 0.707 sin (7.07 × 10^3 t)
- D. 7.07 cos (7.07 × 10^3 t)
Answer: C. 0.707 sin (7.07 × 10^3 t)
Explanation: Resonant frequency ω0 = 1/√(LC) = 1/√(20×10⁻³ × 10⁻⁶) = 7.07 × 10³ rad/s; peak current Im = V0/√(L/C) = 100/141.42 = 0.707 A; i(t) = 0.707 sin(7.07 × 10³ t) A.