A given `LCR` series circuit satisfes the condition for resonance with a given `AC` source. If the angular frequency of the `AC` source is increased by `100%` then in order to establish resonance, and without changing the value of inductance, capacitance must be

Options

A. Increased by `100%`
B. Reduced by `50%`
C. Increased by `75%`
D. Reduced by `75%`

Explanation

To solve the problem step-by-step, we need to analyze the conditions for resonance in an LCR circuit and how changing the angular frequency affects the capacitance.

### Step-by-Step Solution:

1. **Understand the Resonance Condition**:
In an LCR series circuit, resonance occurs when the inductive reactance equals the capacitive reactance. The condition for resonance is given by:
\[
\omega L = \frac{1}{\omega C}
...