In an LC oscillator, \( C = 50\,\mu\mathrm{F} \) and \( L = 0.08\,\mathrm{H} \) are used. If the resistance of the circuit is negligible, the time period of oscillation is
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 12.56 ms
In an LC circuit the charge oscillates between the capacitor and the inductor with angular frequency \( \omega = 1/\sqrt{LC} \), so the time period is
\( \displaystyle T = 2\pi\sqrt{LC} \)
\( L = 0.08\,\mathrm{H} \)
\( C = 50\,\mu\mathrm{F} = 50\times10^{-6}\,\mathrm{F} \)
\( \displaystyle LC = 0.08 \times 50\times10^{-6} = 4\times10^{-6}\,\mathrm{s^{2}} \;\Rightarrow\; \sqrt{LC} = 2\times10^{-3}\,\mathrm{s} \)
\( \displaystyle T = 2\pi \times 2\times10^{-3}\,\mathrm{s} = 4\pi\times10^{-3}\,\mathrm{s} \approx 12.56\,\mathrm{ms} \)
(taking \( \pi = 3.14 \)).
Note: This question is from the pre-rationalised NCERT book (2022-23). The topic was removed from the latest NCERT book (2026-27), and it also appears to be out of the CUET 2026 syllabus.
NCERT (Pre-rationalised edition, 2022-23):
LC Oscillations – “… When a capacitor (initially charged) is connected to an inductor, the charge on the capacitor and the current in the circuit exhibit the phenomenon of electrical oscillations similar to oscillations in mechanical systems.”
LC Oscillations – “… The charge, therefore, oscillates with a natural frequency
\( \displaystyle \omega_0 = \frac{1}{\sqrt{LC}} \qquad (7.41) \)”