Q-factor can be increased by having a coil of

Options

A. Large inductance, small ohmic resistance
B. Large inductance, large ohmic resistance
C. Small inductance, large ohmic resistance
D. Small inductance, small ohmic resistance

Explanation

To solve the question regarding how the Q-factor can be increased by having a coil, let's break it down step by step.

### Step-by-Step Solution:

1. **Understand the Q-factor**:
The Q-factor (Quality factor) of a coil is a measure of its efficiency and is defined as the ratio of the inductive reactance (XL) to the resistance (R) of the coil. The formula for the Q-factor is given by:
\[ Q = \frac{XL}{R} \]

2. **Identify the inductive reactance**:
The inductive reactance (XL) is given by:
\[ XL = \omega L \]
where \( \omega \) is the angular frequency and \( L \) is the inductance of the coil.

3. **Substitute XL into the Q-factor formula**:
Substituting the expression for XL into the Q-factor formula, we get:
\[ Q = \frac{\omega L}{R} \]

4. **Analyze the factors affecting Q**:
From the formula \( Q = \frac{\omega L}{R} \), we can see that:
- To increase the Q-factor, we can either increase the inductance \( L \) or decrease the resistance \( R \).
- This indicates that a higher inductance and lower resistance will lead to a higher Q-factor.

5. **Evaluate the options**:
- **Option 1**: Large inductance, small ohmic resistance – This is correct because both conditions will increase Q.
- **Option 2**: Large ohmic resistance – This is incorrect because increasing resistance would decrease Q.
- **Option 3**: Large ohmic resistance and small inductance – This is incorrect for the same reason as option 2.
- **Option 4**: Small ohmic resistance, small inductance – This is partially correct; while small resistance is good, small inductance does not help in increasing Q.

6. **Conclusion**:
The best option to increase the Q-factor is to have a coil with large inductance and small ohmic resistance. Therefore, the correct answer is:
**Option 1: Large inductance, small ohmic resistance.**