A: At any instant, if the current through an inductor is zero, then the induced emf will also be zero.
R: In one time constant, the current flows to 37 percent of its maximum value in a series LR circuit.

Options

A. If both Assertion & Reason are true and the reason is the correct explanation of the assertion.
B. If both Assertion & Reason are true but the reason is not the correct explanation of the assertion.
C. If Assertion is true statement but Reason is false.
D. If both Assertion and Reason are false statements.

Answer

To solve the assertion and reason question, we need to analyze both statements separately and determine their validity.

### Step 1: Analyze the Assertion
The assertion states: "At any instant, if the current through an inductor is zero, then the induced emf will also be zero."

- **Understanding Inductors**: An inductor opposes changes in current. When the current through an inductor is zero, it means there is no steady current flowing through it.
- **Induced EMF**: The induced electromotive force (emf) in an inductor is given by Faraday's law of electromagnetic induction, which states that the induced emf (E) is equal to the negative rate of change of magnetic flux (Φ) through the inductor:
\[ E = -\frac{d\Phi}{dt} \]
- **Conclusion**: If the current is zero, it does not necessarily mean that the induced emf is zero. The induced emf can still exist if there is a change in magnetic flux. Therefore, the assertion is **false**.

### Step 2: Analyze the Reason
The reason states: "In one time constant, the current flows to 37 percent of its maximum value in a series LR circuit."

- **Time Constant in LR Circuit**: In a series LR circuit, the current (I) at any time (t) can be expressed as:
\[ I(t) = I_{\text{max}} \left(1 - e^{-\frac{t}{\tau}}\right) \]
where \( \tau \) is the time constant.
- **At One Time Constant**: When \( t = \tau \):
\[ I(\tau) = I_{\text{max}} \left(1 - e^{-1}\right) \approx I_{\text{max}} \times 0.632 \]
This means that at one time constant, the current reaches approximately 63.2% of its maximum value, not 37%.
- **Conclusion**: Therefore, the reason is also **false**.

### Final Conclusion
Both the assertion and the reason are false. Thus, the correct answer is that both statements are false.