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

Options

A. the generator 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, follow these steps:

### Step 1: Understand the Resonant Frequency Formula
The resonant frequency (f₀) of an LCR circuit is given by the formula:
\[ f₀ = \frac{1}{2\pi\sqrt{LC}} \]
where:
- \( L \) is the inductance,
- \( C \) is the capacitance.

### Step 2: Analyze the Relationship Between Resonant Frequency and Capacitance
From the formula, we can see that the resonant frequency is inversely related to the square root of the product of inductance and capacitance. This means:
- If capacitance \( C \) increases, the resonant frequency \( f₀ \) decreases.

### Step 3: Determine How to Increase Capacitance
To increase the capacitance in the circuit, you can add another capacitor. The effective capacitance \( C_{\text{effective}} \) when capacitors are connected in parallel is given by:
\[ C_{\text{effective}} = C_1 + C_2 \]
where \( C_1 \) is the original capacitance and \( C_2 \) is the capacitance of the added capacitor.

### Step 4: Connect the Capacitor in Parallel
To achieve an increase in capacitance, connect an additional capacitor in parallel with the existing capacitor. This will increase the total capacitance and consequently reduce the resonant frequency.

### Step 5: Conclusion
Thus, to reduce the resonant frequency in an LCR series circuit, you should add another capacitor in parallel to the existing capacitor.