Anwser a, b **Problem 8.23**The initial value of the voltage \( v \) in the circuit in Fig. 8.1 is zero, and the initial value of the capacitor current, \( i_c(0^+) \), is 45 mA. The expression for the capacitor current is known to be:\[ i_c(t) = A_1 e^{-200t} + A_2 e^{-800t}, \quad t \geq 0^+, \]when \( R \) is 250 Ω. Find:a) The values of \( \alpha, \omega_0, L, C, A_1, \) and \( A_2 \).\[ \left( \text{Hint:} \quad \frac{di_C(0^+)}{dt} = -\frac{di_L(0^+)}{dt} - \frac{di_R(0^+)}{dt} = -\frac{v(0)}{L} - \frac{1}{R} \frac{i_C(0^+)}{C} \right) \]b) The expression for \( v(t), \, t \geq 0 \).c) The expression for \( i_R(t) \geq 0 \).d) The expression for \( i_L(t) \geq 0 \).

Answered: Image /qna-images/answer/f6f6cd7c-9e48-49d8-806b-d9db1b2d7566.jpg

The initial value of the voltage v in the circuit in Fig. 8.1 is zero, and the initial value of the capacitor current, i(0¹), is 45 mA. The expression for the capacitor current is known to be ic(t) = A₁e-200t + A₂e-800t, t≥ 0+, when R is 250 2. Find a) the values of a, wo, L, C, A₁, and A₂ dic(0*) dt di₁(0¹)__dir(0¹) _ −v(0)_ _1 ic(0¹) L RC dt dt b) the expression for v(t), t≥ 0,

The initial value of the voltage v in the circuit in Fig. 8.1 is zero, and the initial value of the capacitor current, i(0¹), is 45 mA. The expression for the capacitor current is known to be ic(t) = A₁e-200t + A₂e-800t, t≥ 0+, when R is 250 2. Find a) the values of a, wo, L, C, A₁, and A₂ dic(0*) dt di₁(0¹)__dir(0¹) _ −v(0)_ _1 ic(0¹) L RC dt dt b) the expression for v(t), t≥ 0,

Introductory Circuit Analysis (13th Edition)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

Chapter1: Introduction

Section: Chapter Questions

Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...

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