In LCR - circuit if resistance increases, quality factor

Options

A. increases finitely
B. decreases finitely
C. remains constant
D. None of these

Explanation

To solve the problem regarding the change in the quality factor (Q) of an LCR circuit when the resistance (R) increases, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Quality Factor Formula**:
The quality factor (Q) of an LCR circuit is given by the formula:
\[ Q = \frac{\omega_0 L}{R} \]
where:
- \( \omega_0 \) is the angular frequency,
- \( L \) is the inductance,
- \( R \) is the resistance.

2. **Analyze the Effect of Increasing Resistance**:
From the formula, we can see that \( Q \) is directly proportional to the inductance \( L \) and the angular frequency \( \omega_0 \), and inversely proportional to the resistance \( R \).

3. **Determine the Relationship**:
If the resistance \( R \) increases, the denominator of the fraction increases. Since \( Q \) is inversely proportional to \( R \), this means that as \( R \) increases, \( Q \) must decrease.

4. **Conclusion on Quality Factor Change**:
Therefore, when resistance increases, the quality factor \( Q \) decreases. However, it is important to note that this decrease is finite; it cannot decrease infinitely because \( \omega_0 L \) remains constant in the equation.

5. **Final Answer**:
The quality factor decreases finitely when the resistance increases.