Answer:
number of cycles = 4.68 × 10⁴ cycles
Explanation:
In damped RLC oscillation
voltage (V(t)) = V_o\ e^{-\dfrac{tR}{2L}}............(1)
given,
C = 0.17μF = 0.17 × 10⁻⁶ F
R = 1.4 Ω
L = 15 m H = 15 × 10⁻³ H V(t) = V₀/2
From the equation (1)
[tex]\dfrac{V_0}{2} = V_0\ e^{-\dfrac{tR}{2L}}[/tex]
[tex]2 = e^{\dfrac{tR}{2L}}[/tex]
taking log both side
[tex]ln ( 2 ) = \dfrac{tR}{2L}[/tex]
[tex]t = \dfrac{2 L ln(2)}{R}[/tex]
[tex]t = \dfrac{2 \times 15 ln(2)}{1.4}[/tex]
t = 14.85 sec
time period
[tex]T= 2\pi \sqrt{LC}[/tex]
[tex]T= 2\pi \sqrt{0.015 \times 0.17 \times 10^{-6}}[/tex]
T = 3.172 × 10⁻⁴
number of cycle =[tex]\dfrac{t}{T}[/tex]
= [tex]\dfrac{14.85}{3.172 \times 10^{-4}}[/tex]
number of cycles = 4.68 × 10⁴ cycles
