Assertion (A) : when capacitive reactance is less than the inductive reactance in a series LCR circuit, e.m.f. leads the current.
Reason (R) : The angle by which alternating voltage leads the alternating current in series RLC circuit is given by `tan varphi = (X_(L) - X_(C))/(R)`.

Options

A. Both A and R are true and R is the correct explanation of A.
B. Both A and R are true and R is NOT the correct explanation of A.
C. A is true but R is false
D. A is false and R is true

Explanation

To solve the problem, we need to analyze the assertion (A) and the reason (R) provided in the question.

### Step 1: Understanding the Assertion (A)
The assertion states that when capacitive reactance (X_C) is less than inductive reactance (X_L) in a series LCR circuit, the electromotive force (e.m.f.) leads the current.

- In a series LCR circuit, the total impedance (Z) is determined by the resistance (R), inductive reactance (X_L), and capacitive reactance (X_C).
- When X_L > X_C, the circuit behaves inductively, meaning the voltage across the inductor leads the current.

**Conclusion for Step 1**: The assertion is correct because in this case, the e.m.f. (voltage) indeed leads the current.

### Step 2: Understanding the Reason (R)
The reason states that the angle by which the alternating voltage leads the alternating current in a series RLC circuit is given by the formula:
\[ \tan \varphi = \frac{X_L - X_C}{R} \]
where \(\varphi\) is the phase angle.

- This formula is derived from the relationship between the voltages and currents in the circuit. The difference in reactance (X_L - X_C) represents the net reactance, and R is the resistance.
- When X_L > X_C, the phase angle \(\varphi\) is positive, indicating that the voltage leads the current.

**Conclusion for Step 2**: The reason is also correct as it accurately describes how the phase angle is determined in the circuit.

### Step 3: Relationship Between Assertion and Reason
Now we need to determine if the reason correctly explains the assertion.

- Both statements are true: the assertion correctly states the condition under which the e.m.f. leads the current, and the reason correctly provides the mathematical relationship for the phase angle.
- However, the reason does not directly explain why the e.m.f. leads the current; it merely provides a formula for the phase angle without connecting it back to the assertion.

**Final Conclusion**: Both the assertion and the reason are true, but the reason does not adequately explain the assertion.

### Final Answer
- **Assertion (A)**: True
- **Reason (R)**: True
- **Explanation**: R does not explain A.

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