The magnetic potential energy stored in a certain inductor is `25mJ`, when the current in the inductor is `60 mA`. This inductor is of inductance

Options

A. 1.389 H
B. 138.88 H
C. 0.138 H
D. 13.89 H

Explanation

To find the inductance of the inductor given the magnetic potential energy and the current, we can follow these steps:

### Step 1: Write down the given values
- Magnetic potential energy (U) = 25 mJ = \( 25 \times 10^{-3} \) J
- Current (I) = 60 mA = \( 60 \times 10^{-3} \) A

### Step 2: Use the formula for magnetic potential energy
The formula for magnetic potential energy stored in an inductor is given by:
\[ U = \frac{1}{2} L I^2 \]
where:
- \( U \) is the magnetic potential energy,
- \( L \) is the inductance,
- \( I \) is the current.

### Step 3: Rearrange the formula to solve for inductance (L)
We can rearrange the formula to solve for \( L \):
\[ L = \frac{2U}{I^2} \]

### Step 4: Substitute the known values into the formula
Now we substitute the values of \( U \) and \( I \) into the equation:
\[ L = \frac{2 \times (25 \times 10^{-3})}{(60 \times 10^{-3})^2} \]

### Step 5: Calculate \( I^2 \)
First, calculate \( I^2 \):
\[ I^2 = (60 \times 10^{-3})^2 = 3600 \times 10^{-6} = 3.6 \times 10^{-3} \]

### Step 6: Substitute \( I^2 \) back into the equation for \( L \)
Now, substitute \( I^2 \) back into the equation for \( L \):
\[ L = \frac{2 \times (25 \times 10^{-3})}{3.6 \times 10^{-3}} \]

### Step 7: Calculate \( L \)
Now, perform the calculation:
\[ L = \frac{50 \times 10^{-3}}{3.6 \times 10^{-3}} = \frac{50}{3.6} \approx 13.89 \, \text{H} \]

### Step 8: Final answer
Thus, the inductance \( L \) is approximately \( 13.89 \, \text{H} \).