In L-C-R series circuit suppose `omega_(r)` is resonance frequency, then match the following table,
`{:(,,"Table-1",,"Table-2"),(,(A),"If " omegagtomega_(r),(P),"Current will lead the voltage"),(,(B),"If " omega=omega_(r),(Q),"Voltage will lead the current"),(,(C),"If " omega=2omega_(r),(R),X_(L)=2X_(C)),(,(D),"If " omegaltomega_(r),(S),"Current and voltage are in phase"),(,,,(T),"None"):}`

Answer

To solve the problem of matching the conditions of an L-C-R series circuit at different frequencies with their corresponding behaviors, we can follow these steps:

### Step 1: Understanding Resonance Frequency
The resonance frequency, denoted as \( \omega_r \), is the frequency at which the inductive reactance \( X_L \) equals the capacitive reactance \( X_C \). At this frequency, the circuit behaves purely resistively.

### Step 2: Analyzing the Cases
We will analyze the behavior of the circuit under the following conditions:
1. \( \omega > \omega_r \)
2. \( \omega = \omega_r \)
3. \( \omega < \omega_r \)
4. \( \omega = 2\omega_r \)

### Step 3: Matching Conditions with Behaviors

**Case A: \( \omega > \omega_r \)**
- The circuit becomes inductive.
- In an inductive circuit, the voltage leads the current.
- Therefore, A matches with Q.

**Case B: \( \omega = \omega_r \)**
- The circuit is at resonance.
- At resonance, the current and voltage are in phase.
- Therefore, B matches with S.

**Case C: \( \omega = 2\omega_r \)**
- This condition is also greater than \( \omega_r \), so the circuit remains inductive.
- Again, in an inductive circuit, the voltage leads the current.
- Therefore, C matches with Q.

**Case D: \( \omega < \omega_r \)**
- The circuit becomes capacitive.
- In a capacitive circuit, the current leads the voltage.
- Therefore, D matches with P.

### Summary of Matches
- A → Q (If \( \omega > \omega_r \), Voltage leads Current)
- B → S (If \( \omega = \omega_r \), Current and Voltage are in phase)
- C → Q (If \( \omega = 2\omega_r \), Voltage leads Current)
- D → P (If \( \omega < \omega_r \), Current leads Voltage)

### Final Matching Table
- A → Q
- B → S
- C → Q
- D → P