Question 15 of 16beginner🔧 ApplyNumerical1 mark

A charged 30 μ\muF capacitor is connected to a 27 mH inductor. What is the angular frequency of free oscillations of the circuit?

Correct Answer

The angular frequency of free oscillations of the circuit is approximately 1111 rad/s.

Exercise: EXERCISES | Q: 7.6 | (Page 24)
For More Understanding

Explanation

This question tests the concept of LC oscillations from Chapter 7. When a charged capacitor is connected to an inductor, the circuit undergoes free oscillations at the natural angular frequency ω = 1/LC\sqrt{LC}. This is the resonant frequency of an LC circuit where energy oscillates between the electric field of the capacitor and the magnetic field of the inductor.

Solution Steps

  1. Step 1: Identify the given values: Capacitance C = 30 μF = 30×1030 \times 10⁻⁶ F, Inductance L = 27 mH = 27×1027 \times 10⁻³ H

  2. Step 2: Write the formula for angular frequency of free oscillations: ω = 1/LC\sqrt{LC}

  3. Step 3: Calculate LC = 30×1030 \times 10⁻⁶ × 27×1027 \times 10⁻³ = 810×10810 \times 10⁻⁹ = 81×1081 \times 10⁻⁸ F·H

  4. Step 4: Calculate LC\sqrt{LC} = \sqrt{$$81 \times 10$$⁻⁸} = 9×109 \times 10⁻⁴

  5. Step 5: Calculate angular frequency: ω = 1/(9×109 \times 10⁻⁴) = 10⁴/9 ≈\approx 1111 rad/s

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