**Problem 7: Inductor Current Calculation**The problem involves a 200 mH inductor with a given voltage across it as:\[ v(t) = (1 - 3t)e^{-3t} \, \text{mV} \]The task is to find the current flowing through the inductor. It is given that the initial current is:\[ i(0) = 0 \]**Explanation:**1. **Voltage Across an Inductor**: The voltage \( v(t) \) across an inductor is related to the current \( i(t) \) through the differential equation: \[ v(t) = L \frac{di(t)}{dt} \] where \( L \) is the inductance of the inductor.2. **Inductance Value**: Here, \( L = 200 \, \text{mH} = 0.2 \, \text{H} \).3. **Initial Condition**: The initial current through the inductor is zero, \( i(0) = 0 \).To find the current \( i(t) \), one would typically integrate the expression after rearranging the differential equation.

Given L=200 mH Y(t) =(1-3t)e -3t mV =(e-31 -3te-3t) MV Is (t) =1/2 {Y(t)dt

Answered: The voltage across a 200 mH inductor is…

The voltage across a 200 mH inductor is v(t) = (1 – 3t)e¬3tmV. Find the current flowing through the inductor. Assume i (0) = 0. %3D

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

**Problem 7: Inductor Current Calculation**

The problem involves a 200 mH inductor with a given voltage across it as:

\[ v(t) = (1 - 3t)e^{-3t} \, \text{mV} \]

The task is to find the current flowing through the inductor. It is given that the initial current is:

\[ i(0) = 0 \]

**Explanation:**

1. **Voltage Across an Inductor**: The voltage \( v(t) \) across an inductor is related to the current \( i(t) \) through the differential equation:
\[
v(t) = L \frac{di(t)}{dt}
\]
where \( L \) is the inductance of the inductor.

2. **Inductance Value**: Here, \( L = 200 \, \text{mH} = 0.2 \, \text{H} \).

3. **Initial Condition**: The initial current through the inductor is zero, \( i(0) = 0 \).

To find the current \( i(t) \), one would typically integrate the expression after rearranging the differential equation.

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