Assertion: In series, L-C-R voltage across capacitor is always less than the applied voltage.
Reason: In series L-C-R circuit, `V = sqrt((V_R^(2) + (V_(L)^(2)-V_(C)^(2)))`

Options

A. If both Assertion and Reason are true and Reason is the correct explanation of Assertion.
B. If both Assertion and Reason are true 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 true.

Explanation

To solve the problem, we need to analyze the assertion and reason provided in the question regarding a series L-C-R circuit.

### Step 1: Understand the Assertion
The assertion states that "In series, L-C-R voltage across the capacitor is always less than the applied voltage." We need to determine if this statement is true or false.

### Step 2: Analyze the Reason
The reason provided is that "In series L-C-R circuit, V = sqrt((V_R^2 + (V_L^2 - V_C^2)))". This equation relates the total voltage (V) in the circuit to the voltages across the resistor (V_R), inductor (V_L), and capacitor (V_C).

### Step 3: Apply the Voltage Relationship
In a series L-C-R circuit, the total voltage (V) is given by:
\[ V^2 = V_R^2 + (V_L - V_C)^2 \]

This implies that:
\[ V = \sqrt{V_R^2 + (V_L - V_C)^2} \]

### Step 4: Analyze the Capacitor Voltage
From the equation, we can see that the voltage across the capacitor (V_C) is influenced by the voltages across the inductor (V_L) and the resistor (V_R). The relationship shows that V_C can vary depending on the values of V_L and V_R.

### Step 5: Determine the Validity of the Assertion
The assertion claims that V_C is always less than V. However, since V_C can be calculated as:
\[ V_C = V_L - \sqrt{V^2 - V_R^2} \]
it is possible for V_C to be greater than V if V_L is sufficiently large compared to V_R. Therefore, the assertion is not universally true.

### Conclusion
- **Assertion**: False (V_C can be greater than V)
- **Reason**: True (The equation accurately describes the relationship in the circuit)

### Final Answer
The assertion is false, and the reason is true.

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