9. A coil with an inductance of \( 2 \, \text{H} \) carries a current of \( 3 \, \text{A} \). What is the energy stored in the magnetic field of the inductor?
The energy (\( U \)) stored in the magnetic field of an inductor is given by the formula:
\[ U = \frac{1}{2} L I^2 \]
Where:
- \( L = 2 \, \text{H} \): Inductance of the coil
- \( I = 3 \, \text{A} \): Current through the coil
Substitute the given values into the formula:
\[ U = \frac{1}{2} \cdot 2 \cdot (3)^2 \]
First, calculate \( (3)^2 \):
\[ (3)^2 = 9 \]
Now calculate \( U \):
\[ U = \frac{1}{2} \cdot 2 \cdot 9 \]
\[ U = 1 \cdot 9 = 9 \, \text{J} \]
Thus, the energy stored in the magnetic field of the inductor is:
\[ U = 9 \, \text{J} \]
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