Practice portal › Alternating Current › LC Oscillations

A charged 25 μF capacitor is connected to a 10 mH inductor. The angular frequency of free oscillation of the circuit is ______ rad s⁻¹.

Asked in GSEB Board July 2023 · Frequency and current in LC

• (1) 0.24
• (2) 200
• (3) 2.2×10³
• (4) 2000

Step-by-step solution

Why the other options are wrong

• (1) No single slip gives 0.24. Sanity check: LC = 10×10⁻³×25×10⁻⁶ = 2.5×10⁻⁷ s², whose square root is 5×10⁻⁴ s; the reciprocal of that is 2000.
• (2) No single slip gives 200. It is one-tenth of the correct value and would need LC a hundred times larger, 2.5×10⁻⁵ s². Recheck the prefixes: m = 10⁻³ and μ = 10⁻⁶.
• (3) Close to the answer but not equal to it. √LC = 5×10⁻⁴ s exactly, so ω = 2000 rad s⁻¹ exactly; 2.2×10³ would need LC ≈ 2.07×10⁻⁷ s².

Reading this solution needs no sign-in. You only sign in to practise against the clock and keep your progress.