In a series RLC AC circult, the frequency of source can be varied. When frequency is varied gradually in one direction from `f_1` to `f_2`, the power is found to be maximum at `f_1`. When frequency is varied gradually at the other direction from `f_1` to `f_3` , the power is found to be same at `f_1` and `f_3`. Match the proper entries from column-2 to column-1 using the codes given below the columns, (consider `f_1 gt f_2`)
`{:("Column-I",,"Column-II"),("when the frequency is equal to",,"The circuit is or can be"),("AM: arithmatic mean GM:geometic mean",,),("(P) AM of "f_(1) and "f"_(2),,"(1) capacitance"),((Q) "GM of "f_(1) and "f"_(2),,"(2) inductive"),("(R) AM of " f_(1) and "f"_(3),,"(3) resistive"),("(S) GM of " f_(1) and "f"_(3),,"(4) at resonance"):}`

Options

A. `{:(,P,Q,R,S),((A),4,3,2,4):}`
B. `{:(,P,Q,R,S),((B),3,1,3,2):}`
C. `{:(,P,Q,R,S),((C),2,1,2,3):}`
D. `{:(,P,Q,R,S),((D),1,1,2,4):}`

Explanation

To solve the problem, we need to analyze the relationships between the frequencies \( f_1 \), \( f_2 \), and \( f_3 \) in the context of an RLC circuit and how they relate to the types of circuits (capacitive, inductive, resistive) at different frequencies.

### Step-by-Step Solution:

1. **Understanding the Resonance Condition**:
- In an RLC circuit, resonance occurs at a frequency \( f_r = \frac{1}{2\pi\sqrt{LC}} \). At this frequency, the impedance is minimized, and the circuit behaves purely resistively.

2. **Analyzing the Given Frequencies**:
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