Free electromagnetic oscillations occur in an electrical circuit. Knowing the characteristic dimensions of the elements, L=20mH și C=0,005mF, determine: a)The period of free electromagnetic oscillations: b)Frequency of free electromagnetic oscillations: c)Electromagnetic energy in the circuit when the maximum value of the current intensity is equal to 100 mA.

a. 0.199 ms b. 5.03 kHz c. 0.1 mJ

Explanation:

a. The period of oscillation of an L-C circuit is T = 2π√(LC) where L = inductance = 20 mH = 20 × 10⁻³ H and C = capacitance = 0.005 mF = 5 × 10⁻⁶ F.

So, T = 2π√(LC)

= 2π√(20 × 10⁻³ H × 5 × 10⁻⁶ F)

= 2π√(100 × 10⁻¹¹)

= 2π√(10 × 10⁻¹⁰)

= 2π(3.16 × 10⁻⁵)

= 19.87 × 10⁻⁵

= 1.987 × 10⁻⁴ s

= 1.99 × 10⁻⁴ s

= 0.199 × 10⁻³ s

= 0.199 ms

b. frequency , f = 1/T where T = period = 0.199 × 10⁻³ s.

So, f = 1/0.199 × 10⁻³ s

= 5.03 × 10³ Hz

= 5.03 kHz

c. The electromagnetic energy E = 1/2Li² where L = inductance = 20 × 10⁻³ H and i = current = 100 mA = 0.1 A

So, E = 1/2Li²

= 1/2 × 20 × 10⁻³ H × (0.1 A)²

= 0.1 × 10⁻³ J

= 0.1 mJ

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