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A charged 10 μF capacitor is connected to a 16 mH inductor. What is the angular frequency of free oscillations of the circuit?

Asked in GUJCET 2022 · Frequency and current in LC

• (1) 250 rad s⁻¹
• (2) 25 rad s⁻¹
• (3) 1111 rad s⁻¹
• (4) 2500 rad s⁻¹

Step-by-step solution

Why the other options are wrong

• (1) No single slip produces 250 rad s⁻¹, which is ten times too small. Sanity check: LC=16×10⁻³×10×10⁻⁶=1.6×10⁻⁷ s² and ω=1/(√LC)=2500 rad s⁻¹.
• (2) No single slip produces 25 rad s⁻¹, which is a hundred times too small. Sanity check: √1.6×10⁻⁷=4×10⁻⁴ s, so ω=2500 rad s⁻¹.
• (3) 1111 rad s⁻¹ is what 1/(√LC) gives for 30 μF and 27 mH, the numbers in the textbook version of this question. With 10 μF and 16 mH it is 2500 rad s⁻¹.

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