Answer:
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
To solve this problem , we will use the length contraction equation as follows:
L = L0((1 - v^2/c^2))^0.5
where:
L is the desired length
L0 is the length measured at initial frame = 1 m
v is the velocity
c is the speed of light
Substituting by these givens in the above equation, we can calculate L as follows:
L = 1((1 - (0.8 c)^2/c2))^0.5 = 0.6 meters
The mechanical energy changes into the electrical energy.
