To reduce the resonant frequency in an `LCR` series circuit with a generator

Options

A. the galvanometer frequency should be reduced
B. another capacitor should be added in parallel to the first
C. the iron core of the inductor should be removed
D. dielectric in the capacitor should be removed.

Explanation

To reduce the resonant frequency in an LCR series circuit with a generator, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Resonant Frequency Formula**:
The resonant frequency \( f \) of a series LCR circuit is given by the formula:
\[ f = \frac{1}{2\pi \sqrt{LC}} \]
where \( L \) is the inductance and \( C \) is the capacitance.

2. **Identify the Relationship**:
From the formula, we can see that the resonant frequency \( f \) is inversely proportional to the square root of the product of inductance \( L \) and capacitance \( C \). This means:
\[ f \propto \frac{1}{\sqrt{C}} \]
Therefore, to reduce the resonant frequency, we need to increase the capacitance \( C \).

3. **Increase Capacitance**:
To increase the capacitance in the circuit, we can add additional capacitors. There are two ways to connect capacitors: in series and in parallel.

4. **Choose the Connection Method**:
- **Parallel Connection**: When capacitors are connected in parallel, the effective capacitance \( C_{eff} \) is given by:
\[ C_{eff} = C_1 + C_2 + C_3 + \ldots \]
This method increases the total capacitance, which will help in reducing the resonant frequency.

- **Series Connection**: When capacitors are connected in series, the effective capacitance is given by:
\[ \frac{1}{C_{eff}} = \frac{1}{C_1} + \frac{1}{C_2} + \ldots \]
This method results in a smaller effective capacitance, which is not desirable for our goal of reducing the resonant frequency.

5. **Conclusion**:
To effectively reduce the resonant frequency in the LCR circuit, we should connect additional capacitors in parallel to increase the overall capacitance.