If emf induced in a coil is 2V by changing the current in it from 8 A to 6 A in `2 xx 10^(3)` s . Then , the coefficient of self -induction is

Options

A. `2xx10^(-3)H`
B. `10^(-3)H`
C. `0.5xx10^(-3)H`
D. `4xx10^(-3)H`

Explanation

To find the coefficient of self-induction (L) in the given problem, we can follow these steps:

### Step 1: Identify the given values
- Induced EMF (E) = 2 V
- Initial current (I_initial) = 8 A
- Final current (I_final) = 6 A
- Time (t) = 2 × 10^3 s

### Step 2: Calculate the change in current (ΔI)
The change in current (ΔI) can be calculated as:
\[ \Delta I = I_{\text{initial}} - I_{\text{final}} = 8 \, \text{A} - 6 \, \text{A} = 2 \, \text{A} \]

### Step 3: Use the formula for induced EMF
The formula for the induced EMF in terms of self-inductance is given by:
\[ E = L \frac{\Delta I}{\Delta t} \]
Where:
- \(E\) is the induced EMF,
- \(L\) is the self-inductance,
- \(\Delta I\) is the change in current,
- \(\Delta t\) is the time interval.

### Step 4: Rearrange the formula to solve for L
We can rearrange the formula to find L:
\[ L = \frac{E \cdot \Delta t}{\Delta I} \]

### Step 5: Substitute the known values into the equation
Substituting the known values into the equation:
\[ L = \frac{2 \, \text{V} \cdot (2 \times 10^3 \, \text{s})}{2 \, \text{A}} \]

### Step 6: Simplify the equation
Calculating the right-hand side:
\[ L = \frac{2 \cdot 2 \times 10^3}{2} = 2 \times 10^3 \, \text{H} \]

### Step 7: Final answer
Thus, the coefficient of self-induction \(L\) is:
\[ L = 2 \times 10^3 \, \text{H} \]