A current of 10A in the primary coil of a circuit is reduced to zero. If the coefficient of mutual inductance is 3 H and emf induced in the secondary coil is 30 kV, time taken for the change of current is

Options

A. `10^3 s`
B. `10^2 s`
C. `10^(-3)s`
D. `10^(-2)s`

Answer

To solve the problem, we need to find the time taken for the current in the primary coil to change from 10 A to 0 A, given the mutual inductance and the induced EMF in the secondary coil.

### Step-by-Step Solution:

1. **Identify the given values:**
- Current in the primary coil (I) changes from 10 A to 0 A.
- Coefficient of mutual inductance (M) = 3 H.
- Induced EMF in the secondary coil (E) = 30 kV = 30,000 V.

2. **Use the formula for induced EMF:**
The induced EMF (E) in the secondary coil due to the change in current in the primary coil can be expressed as:
\[ E = -M \frac{dI}{dt} \]
where \(dI\) is the change in current and \(dt\) is the time taken for that change.

3. **Calculate the change in current (dI):**
The change in current \(dI\) is:
\[ dI = I_{final} - I_{initial} = 0 A - 10 A = -10 A \]

4. **Substitute the values into the EMF formula:**
Rearranging the formula for \(dt\):
\[ dt = -M \frac{dI}{E} \]
Substituting the known values:
\[ dt = -3 \, \text{H} \cdot \frac{-10 \, \text{A}}{30,000 \, \text{V}} \]

5. **Calculate dt:**
\[ dt = \frac{3 \cdot 10}{30,000} = \frac{30}{30,000} = \frac{1}{1,000} = 0.001 \, \text{s} = 10^{-3} \, \text{s} \]

6. **Final Answer:**
The time taken for the change of current is:
\[ dt = 10^{-3} \, \text{s} = 1 \, \text{ms} \]