Assertion : In the phenomenon of mutual induction, self induction of each of the coils persists.
Reason : Self induction arises when strength of current in same coil changes. In mutual induction, current is changing in both the individual coils.

Explanation

To solve the question, we need to analyze the assertion and reason provided:

### Assertion:
In the phenomenon of mutual induction, self-induction of each of the coils persists.

### Reason:
Self-induction arises when the strength of the current in the same coil changes. In mutual induction, current is changing in both the individual coils.

### Step-by-Step Solution:

1. **Understanding Mutual Induction**:
- Mutual induction occurs when a change in current in one coil induces an electromotive force (emf) in another coil that is magnetically linked to it.
- When current (I1) flows through coil 1, it generates a magnetic field (B1), which links with coil 2, inducing an emf (E2) in coil 2.

**Hint**: Recall that mutual induction involves two coils influencing each other through their magnetic fields.

2. **Self-Induction in Coils**:
- Self-induction refers to the phenomenon where a change in current in a coil induces an emf in the same coil due to its own changing magnetic field.
- When the current in coil 2 changes (due to the induced emf from coil 1), it generates its own magnetic field (B2) and induces an emf in itself (self-induction, S2).

**Hint**: Remember that self-induction is about a coil responding to its own changing current.

3. **Evaluating the Assertion**:
- The assertion states that self-induction persists in both coils during mutual induction. This is true because even though the coils are influencing each other, each coil still experiences self-induction due to its own changing current.

**Hint**: Consider how each coil behaves independently while also being affected by the other.

4. **Evaluating the Reason**:
- The reason explains that self-induction arises from a change in current in the same coil and states that in mutual induction, currents in both coils are changing. This is also true.
- However, the reason does not directly explain why self-induction persists in both coils during mutual induction. It merely states facts about self-induction and mutual induction without linking them.

**Hint**: Analyze whether the reason logically connects to the assertion or simply states related facts.

5. **Conclusion**:
- Both the assertion and the reason are true statements. However, the reason is not the correct explanation for the assertion. Therefore, the answer is that the assertion is true, the reason is true, but the reason is not the correct explanation of the assertion.

### Final Answer:
- The assertion is true, the reason is true, but the reason is not the correct explanation of the assertion. Thus, the answer is option number 2.