An RLC circuit has different time constants for switch configurations S₁ and S₂: 0.05 s and 2 s. Closing S₃ instead causes free oscillations. Find oscillation period T (s) using the circuit shown. [See Image.]
Physics · Mixed Chapter
JEE Main Practice

Question

An RLC circuit has different time constants for switch configurations S₁ and S₂: 0.05 s and 2 s. Closing S₃ instead causes free oscillations. Find oscillation period T (s) using the circuit shown. [See Image.]

Physics · Mixed Chapter

G1 Physics · Accepted Answer

Step 1 — For one R–C switch setting, the measured time constant is τ₍RC₎ = RC = 0.05 s. Step 2 — For R–L setting, τ₍RL₎ = L/R = 2 s. Step 3 — Multiply: LC = (RC)(L/R) = 0.10 s². Step 4 — Undamped resonant period T = 2π√(LC) = 2π√0.10 ≈ 1.99 s, so T≈2 s.