### Magnetic Energy Stored in an Inductor**Problem Statement:**Find the magnetic energy stored by a 5.22 mH inductor when the current through it is 11.1 A.Use the formula for the energy stored in an inductor:\[ W = \frac{1}{2} L I^2 \]Where:- \( W \) is the energy stored (in joules),- \( L \) is the inductance (in henries, H),- \( I \) is the current (in amperes, A).### Solution:1. Convert the inductance into henries:\[ L = 5.22 \text{ mH} = 5.22 \times 10^{-3} \text{ H} \]2. Substitute the values into the formula:\[ W = \frac{1}{2} \times 5.22 \times 10^{-3} \text{ H} \times (11.1 \text{ A})^2 \]3. Carry out the calculations:\[ W = \frac{1}{2} \times 5.22 \times 10^{-3} \text{ H} \times 123.21 \text{ A}^2 \]\[ W = 0.5 \times 5.22 \times 10^{-3} \times 123.21 \]\[ W \approx 0.3216 \text{ J} \]**Answer:**\[ \boxed{W \approx 0.3216 \text{ J}} \]

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Find the magnetic energy stored by a 5.22 mH inductor when the current through it is 11.1 A.

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Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

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Concept explainers

Voltage Across Inductor

An actor is a passive electrical component that consists of a coil bent in the form of wire which uses electromagnetism to produce electric current through the coil. When the electric current flows through a conductor that is the coil, a magnetic flux is developed around the conductor. This flow of current through the coil creates a magnetic field based on Fleming's Right-hand thumb rule. If there is any decrease in the current passing through the inductor, then the magnetic field will also decrease and energy is released through the generation of electric current. There is also a secondary voltage inducing in the same coil due to the magnetic flux, since it opposes any changes in the electric current flowing through the circuit. An inductor is also called choke, coil, or solenoid. A choke is designed to block certain frequencies when the DC current passes. A winding coil is coated with insulation to give extra insulation and protect the circuit. They are usually tightly wrapped around a central core which is cylindrical in nature so that the magnetic flux can be induced. The solenoid is a three-dimension coil that is used to exhibit electromagnetism when the magnetic field is developed due to the current flowing through the coil. The sign convention of the inductor is the same as the power dissipating device. When the current flows into the positive side of the voltage across the inductor, the value is positive and the inductor dissipates power whereas when the inductor releases the power back to the circuit, the current has a negative sign convention. 

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### Magnetic Energy Stored in an Inductor

**Problem Statement:**
Find the magnetic energy stored by a 5.22 mH inductor when the current through it is 11.1 A.

Use the formula for the energy stored in an inductor:
\[ W = \frac{1}{2} L I^2 \]

Where:
- \( W \) is the energy stored (in joules),
- \( L \) is the inductance (in henries, H),
- \( I \) is the current (in amperes, A).

### Solution:
1. Convert the inductance into henries:
\[ L = 5.22 \text{ mH} = 5.22 \times 10^{-3} \text{ H} \]
2. Substitute the values into the formula:
\[ W = \frac{1}{2} \times 5.22 \times 10^{-3} \text{ H} \times (11.1 \text{ A})^2 \]
3. Carry out the calculations:
\[ W = \frac{1}{2} \times 5.22 \times 10^{-3} \text{ H} \times 123.21 \text{ A}^2 \]
\[ W = 0.5 \times 5.22 \times 10^{-3} \times 123.21 \]
\[ W \approx 0.3216 \text{ J} \]

**Answer:**
\[ \boxed{W \approx 0.3216 \text{ J}} \]

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