(L11) The current flowing through a 3.64E-3 H inductor increases from 3.50 A to 9.62 A. What is the work done by the current to the inductor (in J)?
(L11) The current flowing through a 3.64E-3 H inductor increases from 3.50 A to 9.62 A. What is the work done by the current to the inductor (in J)?
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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![**Question (L11):** The current flowing through a 3.64E-3 H inductor increases from 3.50 A to 9.62 A. What is the work done by the current to the inductor (in J)?
*Note:* This question focuses on calculating the work done on an inductor when the current flowing through it changes. The given inductance value is 3.64E-3 Henries. The initial and final current values are 3.50 Amperes and 9.62 Amperes, respectively.
**Explanation:**
Inductance is a property of an electrical conductor which determines the amount of electromotive force generated for a given change in the current flowing through it, expressed in Henry (H). When the current flowing through an inductor changes, energy is stored in the magnetic field created by the inductor. The work done on the inductor is equivalent to the energy stored in the inductor.
**Formula:**
The energy (W) stored in an inductor is given by the formula:
\[ W = \frac{1}{2} L (I_f^2 - I_i^2) \]
where,
- \( L \) is the inductance in Henries (H),
- \( I_f \) is the final current in Amperes (A),
- \( I_i \) is the initial current in Amperes (A).
**Given Data:**
- Inductance, \( L = 3.64 \times 10^{-3} \, H \)
- Initial current, \( I_i = 3.50 \, A \)
- Final current, \( I_f = 9.62 \, A \)
**Calculation:**
1. Substitute the given values into the formula:
\[ W = \frac{1}{2} \times 3.64 \times 10^{-3} \, H \times (9.62^2 - 3.50^2) \]
2. Calculate the square of the currents:
\[ 9.62^2 = 92.5444 \]
\[ 3.50^2 = 12.25 \]
3. Find the difference between the squares of the currents:
\[ 92.5444 - 12.25 = 80.2944 \]
4. Multiply this difference by the inductance](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6401e82b-1884-43b6-8725-0773860dca12%2F1904cd75-0a8c-4fae-a1e3-a91a5f43c8ba%2F7mx5yoe_processed.png&w=3840&q=75)
Transcribed Image Text:**Question (L11):** The current flowing through a 3.64E-3 H inductor increases from 3.50 A to 9.62 A. What is the work done by the current to the inductor (in J)?
*Note:* This question focuses on calculating the work done on an inductor when the current flowing through it changes. The given inductance value is 3.64E-3 Henries. The initial and final current values are 3.50 Amperes and 9.62 Amperes, respectively.
**Explanation:**
Inductance is a property of an electrical conductor which determines the amount of electromotive force generated for a given change in the current flowing through it, expressed in Henry (H). When the current flowing through an inductor changes, energy is stored in the magnetic field created by the inductor. The work done on the inductor is equivalent to the energy stored in the inductor.
**Formula:**
The energy (W) stored in an inductor is given by the formula:
\[ W = \frac{1}{2} L (I_f^2 - I_i^2) \]
where,
- \( L \) is the inductance in Henries (H),
- \( I_f \) is the final current in Amperes (A),
- \( I_i \) is the initial current in Amperes (A).
**Given Data:**
- Inductance, \( L = 3.64 \times 10^{-3} \, H \)
- Initial current, \( I_i = 3.50 \, A \)
- Final current, \( I_f = 9.62 \, A \)
**Calculation:**
1. Substitute the given values into the formula:
\[ W = \frac{1}{2} \times 3.64 \times 10^{-3} \, H \times (9.62^2 - 3.50^2) \]
2. Calculate the square of the currents:
\[ 9.62^2 = 92.5444 \]
\[ 3.50^2 = 12.25 \]
3. Find the difference between the squares of the currents:
\[ 92.5444 - 12.25 = 80.2944 \]
4. Multiply this difference by the inductance
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