Respuesta :
Answer:
Explanation:
This is the case of L-R charging circuit , for which the formula is as follows
i = i₀ ( 1 - [tex]e^{\frac{-t}{\tau}[/tex] )
Differentiating the equation on both sides
di / dt = i₀ / τ x [tex]e^\frac{-t}{\tau}[/tex]
i is current at time t , i₀ is maximum current , τ is time constant which is equal to L / R where L is inductance and R is resistance of the circuit .
τ = L / R = 9 x 10⁻³ / 230
= 39 x 10⁻⁶ s
i₀ = 12 / 230 = 52.17 x 10⁻³
di / dt (at t is zero) = 52.17 x 10⁻³ / 39 x 10⁻⁶
= 1.33 x 10³ A / s
Time to reach 85 % of steady state or i₀
.85 = [tex]1 - e^\frac{t}{\tau}[/tex]
[tex]e^\frac{-t}{\tau}[/tex] = .15
t / τ = ln .15
t = 74 μs
