If the current i(t) = 6t A/s flows through a 9 H inductor, find the current flowing and the energy stored at t = 2 s. Current = A Energy = J
If the current i(t) = 6t A/s flows through a 9 H inductor, find the current flowing and the energy stored at t = 2 s. Current = A Energy = J
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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![### Problem Statement
If the current \( i(t) = 6t \, \text{A/s} \) flows through a \( 9 \, \text{H} \) inductor, find the current flowing and the energy stored at \( t = 2 \, \text{s} \).
### Solution
1. **Current Calculation**
To find the current \( I \) at \( t = 2 \, \text{s} \):
\( I = i(t) = 6t \)
Substitute \( t = 2 \):
\( I = 6 \times 2 = 12 \, \text{A} \)
**Current =** \[ \boxed{12} \] A
2. **Energy Stored Calculation**
The energy \( W \) stored in an inductor is given by:
\[
W = \frac{1}{2} L I^2
\]
Where \( L = 9 \, \text{H} \) and \( I = 12 \, \text{A} \).
\[
W = \frac{1}{2} \times 9 \times (12)^2
\]
\[
W = \frac{1}{2} \times 9 \times 144
\]
\[
W = \frac{1}{2} \times 1296
\]
\[
W = 648 \, \text{J}
\]
**Energy =** \[ \boxed{648} \] J
This educational content guides students to calculate the current and energy stored in an inductor for a given time, using provided formulas.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0c42d3d3-c669-4ebd-a92e-b9a728000a05%2F1cff599f-53e6-41b3-ab2b-a277c603e0ec%2Fwnf89u8_processed.png&w=3840&q=75)
Transcribed Image Text:### Problem Statement
If the current \( i(t) = 6t \, \text{A/s} \) flows through a \( 9 \, \text{H} \) inductor, find the current flowing and the energy stored at \( t = 2 \, \text{s} \).
### Solution
1. **Current Calculation**
To find the current \( I \) at \( t = 2 \, \text{s} \):
\( I = i(t) = 6t \)
Substitute \( t = 2 \):
\( I = 6 \times 2 = 12 \, \text{A} \)
**Current =** \[ \boxed{12} \] A
2. **Energy Stored Calculation**
The energy \( W \) stored in an inductor is given by:
\[
W = \frac{1}{2} L I^2
\]
Where \( L = 9 \, \text{H} \) and \( I = 12 \, \text{A} \).
\[
W = \frac{1}{2} \times 9 \times (12)^2
\]
\[
W = \frac{1}{2} \times 9 \times 144
\]
\[
W = \frac{1}{2} \times 1296
\]
\[
W = 648 \, \text{J}
\]
**Energy =** \[ \boxed{648} \] J
This educational content guides students to calculate the current and energy stored in an inductor for a given time, using provided formulas.
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