Assertion An induced emf of 2 V is developed in a circular loop, if current in the loop is changed at a rate of 4 `As^(-1)` .IF 4 A of current is passed through this loop, then flux linked with this coil will be 2 Wb.
Reason Flux linked with the coil is
`|phi|=|(e)/(di//dt)|i`

Options

A. If both Assertion and Reason are corrent and Reason is the corrent explanation of Assertion.
B. If both Assertion and Reason are correct but Reason is not the correct explanation of Assertion.
C. If Assertion is true but Reason is false.
D. If Assertion is false but Reason is ture.

Explanation

To solve the given problem, we will analyze both the assertion and the reason step by step.

### Step 1: Understanding the Given Information
We are provided with:
- An induced emf (E) of 2 V.
- A rate of change of current (di/dt) of 4 A/s.
- A current (I) of 4 A flowing through the loop.

### Step 2: Using the Formula for Induced EMF
The induced emf in a coil can be expressed using the formula:
\[ E = L \frac{di}{dt} \]
where \( L \) is the inductance of the coil.

### Step 3: Rearranging the Formula to Find Inductance
From the formula above, we can rearrange it to find the inductance \( L \):
\[ L = \frac{E}{\frac{di}{dt}} \]
Substituting the known values:
\[ L = \frac{2 \, \text{V}}{4 \, \text{A/s}} = 0.5 \, \text{H} \]

### Step 4: Finding the Magnetic Flux Linked with the Coil
The magnetic flux \( \Phi \) linked with the coil can be expressed as:
\[ \Phi = L \cdot I \]
Substituting the values we have:
\[ \Phi = 0.5 \, \text{H} \cdot 4 \, \text{A} = 2 \, \text{Wb} \]

### Step 5: Conclusion
The assertion states that the flux linked with the coil will be 2 Wb, which we have calculated to be true. Therefore, the assertion is correct.

### Step 6: Validating the Reason
The reason provided states that:
\[ |\Phi| = \left|\frac{E}{\frac{di}{dt}}\right| I \]
This is consistent with our calculations since we derived that:
\[ \Phi = L \cdot I \]
and \( L \) was calculated as \( \frac{E}{\frac{di}{dt}} \). Thus, the reason is also correct.

### Final Answer
Both the assertion and the reason are true, and the reason correctly explains the assertion.

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