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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)
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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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 \( i_L(t) \geq 0 \).
Transcribed Image Text:**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 \( i_L(t) \geq 0 \).
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