The dimensions of self inductance are

Options

A. `[MLT^-2A^-2]`
B. `[ML^2T^-1A^-2]`
C. `[ML^2T^-2A^-2]`
D. `[ML^2T^-2A^-1]`

Explanation

To find the dimensions of self-inductance, we can follow these steps:

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

### Step 2: Rearrange the formula to express self-inductance
From the formula, we can express self-inductance \( L \) as:
\[ L = \frac{2U}{I^2} \]

### Step 3: Identify the dimensions of energy and current
- The dimension of energy \( U \) is given by:
\[ [U] = [M][L^2][T^{-2}] \]
where \( M \) is mass, \( L \) is length, and \( T \) is time.

- The dimension of current \( I \) is given by:
\[ [I] = [A] \]
where \( A \) is the dimension of electric current.

### Step 4: Substitute the dimensions into the expression for self-inductance
Now substituting the dimensions of \( U \) and \( I \) into the expression for \( L \):
\[ [L] = \frac{[U]}{[I]^2} = \frac{[M][L^2][T^{-2}]}{[A]^2} \]

### Step 5: Simplify the expression
Thus, the dimensions of self-inductance \( L \) can be written as:
\[ [L] = [M][L^2][T^{-2}][A^{-2}] \]

### Final Answer
The dimensions of self-inductance are:
\[ [L] = [M][L^2][T^{-2}][A^{-2}] \]

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