write the unit of self inductance

Options

A. `1 Å`
B. `10^(-11) cm`
C. `10^(-12) cm`
D. `10^(-15) cm`

Explanation

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

### Step 1: Understand the Concept of Self-Inductance
Self-inductance is a property of a coil or circuit that quantifies its ability to induce an electromotive force (emf) in itself due to a change in current.

**Hint:** Remember that self-inductance relates to how a changing current generates a voltage.

### Step 2: Identify the Standard Unit
The standard unit of self-inductance is defined as the amount of inductance that will induce an emf of one volt when the current through the inductor changes at a rate of one ampere per second.

**Hint:** Think about the relationship between voltage, current, and the rate of change of current.

### Step 3: Write the Unit in Terms of Basic Units
The unit of self-inductance can be expressed in terms of Weber per Ampere (Wb/A).

**Hint:** Recall that Weber (Wb) is the unit of magnetic flux, and Ampere (A) is the unit of electric current.

### Step 4: Alternative Unit Representation
Self-inductance can also be represented in terms of Henry (H), which is defined as 1 H = 1 Wb/A.

**Hint:** Consider how different units can represent the same physical quantity.

### Step 5: Provide the Dimensional Formula
The dimensional formula for self-inductance can be derived from its definition. It is given as:

\[ [L] = M^1 L^2 T^{-2} A^{-2} \]

This means:
- M = Mass
- L = Length
- T = Time
- A = Electric Current

**Hint:** Remember that dimensional analysis helps in understanding the relationship between different physical quantities.

### Final Answer
The unit of self-inductance is:
- Weber per Ampere (Wb/A) or
- Henry (H)