**Title: Analyzing an RLC Circuit****Text:**For the circuit below with \( R = 12.5\Omega \), \( L = 25\text{mH} \), \( C = 62.5\mu\text{F} \). Assume that at the instant that the 2A current source is applied to the circuit, the initial inductor current is 1A and that the initial capacitor voltage is 50V. Find the expression for \( i_L(t) \) for \( t \geq 0 \).**Diagram Explanation:**- **Current Source (2 A):** The circuit is powered by a 2A current source. - **Capacitor (C):** The capacitor has a capacitance of 62.5 μF and is initially charged to 50V. It is oriented such that the positive side is connected upwards.- **Inductor (L):** The inductor with an inductance of 25 mH has an initial current of 1A flowing through it.- **Resistor (R):** The resistor has a resistance of 12.5 Ω.- **Current Directions:** - \( i_C \) represents the current through the capacitor. - \( i_L \) represents the current through the inductor. - \( i_R \) represents the current through the resistor. - \( I_0 \) represents the initial conditions related to this circuit.The goal is to determine the time-dependent expression for the current through the inductor, \( i_L(t) \), starting at \( t = 0 \).

The given circuit isThe initial inductor current, iL(0−)=1 A.The initial capacitor voltage,…

For the circuit below with R= 12.50, L = 25mH, C = 62.5µF. Assume that at the instant that the 2A current source is applied to the circuit, the initial inductor current is 1A and that the initial capacitor voltage is 50V. Find the expression for i(t) for t≥ 0. i_C i_RI 2 A 4 62.5 μF L 25 mH 10 R 12.5 Ω m

For the circuit below with R= 12.50, L = 25mH, C = 62.5µF. Assume that at the instant that the 2A current source is applied to the circuit, the initial inductor current is 1A and that the initial capacitor voltage is 50V. Find the expression for i(t) for t≥ 0. i_C i_RI 2 A 4 62.5 μF L 25 mH 10 R 12.5 Ω m

Introductory Circuit Analysis (13th Edition)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

Chapter1: Introduction

Section: Chapter Questions

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Question

**Title: Analyzing an RLC Circuit**

**Text:**

For the circuit below with \( R = 12.5\Omega \), \( L = 25\text{mH} \), \( C = 62.5\mu\text{F} \). Assume that at the instant that the 2A current source is applied to the circuit, the initial inductor current is 1A and that the initial capacitor voltage is 50V. Find the expression for \( i_L(t) \) for \( t \geq 0 \).

**Diagram Explanation:**

- **Current Source (2 A):** The circuit is powered by a 2A current source.

- **Capacitor (C):** The capacitor has a capacitance of 62.5 μF and is initially charged to 50V. It is oriented such that the positive side is connected upwards.

- **Inductor (L):** The inductor with an inductance of 25 mH has an initial current of 1A flowing through it.

- **Resistor (R):** The resistor has a resistance of 12.5 Ω.

- **Current Directions:**
- \( i_C \) represents the current through the capacitor.
- \( i_L \) represents the current through the inductor.
- \( i_R \) represents the current through the resistor.
- \( I_0 \) represents the initial conditions related to this circuit.

The goal is to determine the time-dependent expression for the current through the inductor, \( i_L(t) \), starting at \( t = 0 \).

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Step 1: Summarize the data.

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Step 2: Determine the differential equation for t > 0.

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Step 3: Determine the generalized expression of i_L(t).

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Step 4: Determine the expression of i_L(t) for t >= 0.

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