The current in ampere through an inductor is
i=(20t+10)
Here t is in second. The induced emf in the inductor 4V.
Total flux linked with the inductor at t= 2 is a

Options

A. 10 Wb
B. 20 Wb
C. 30 Wb
D. 40 Wb

Answer

To solve the problem, we need to find the total flux linked with the inductor at \( t = 2 \) seconds given the current \( i(t) = 20t + 10 \) and the induced emf \( \mathcal{E} = 4 \) volts.

### Step-by-Step Solution:

1. **Identify the given information:**
- Current through the inductor: \( i(t) = 20t + 10 \)
- Induced emf: \( \mathcal{E} = 4 \) volts

2. **Use the formula for induced emf:**
The induced emf in an inductor is given by the formula:
\[ \mathcal{E} = L \frac{di}{dt} \]
where \( L \) is the inductance and \( \frac{di}{dt} \) is the rate of change of current with respect to time.

3. **Differentiate the current with respect to time:**
We need to find \( \frac{di}{dt} \):
\[ i(t) = 20t + 10 \]
Differentiating:
\[ \frac{di}{dt} = 20 \]

4. **Substitute into the emf formula:**
Now substitute \( \frac{di}{dt} \) into the induced emf equation:
\[ 4 = L \cdot 20 \]

5. **Solve for inductance \( L \):**
Rearranging the equation gives:
\[ L = \frac{4}{20} = \frac{1}{5} \text{ Henry} \]

6. **Calculate the current at \( t = 2 \) seconds:**
Substitute \( t = 2 \) into the current equation:
\[ i(2) = 20(2) + 10 = 40 + 10 = 50 \text{ A} \]

7. **Calculate the total flux \( \Phi \):**
The total flux linked with the inductor is given by:
\[ \Phi = L \cdot i \]
Substitute the values of \( L \) and \( i \):
\[ \Phi = \frac{1}{5} \cdot 50 = 10 \text{ Weber} \]

### Final Answer:
The total flux linked with the inductor at \( t = 2 \) seconds is \( 10 \) Weber.