Correct : b

Circuit Description:
This is a Wien Bridge Oscillator circuit with:
• An ideal op-amp
• Feedback resistor R_f from output to inverting input
• Resistor R from inverting input to ground
• Series RC network (C and R) in the positive feedback path
• Parallel RC network (R and C) to ground

For a Wien Bridge Oscillator to produce sustained oscillations, two conditions must be satisfied:

Condition 1: Frequency of Oscillation
The frequency at which the circuit oscillates is determined by the RC network in the positive feedback path.

At the resonant frequency, the phase shift through the RC network is zero, and this occurs when:
f = 1/(2πRC)

Condition 2: Barkhausen Criterion for Sustained Oscillation
For sustained oscillations, the loop gain must equal 1, and the total phase shift around the loop must be 0° (or 360°).

The gain of the RC feedback network at resonance is 1/3.
Therefore, the amplifier gain must be 3 to compensate.

The non-inverting amplifier gain is:
A = 1 + (R_f/R)

Setting this equal to 3:
1 + (R_f/R) = 3
R_f/R = 2
R_f = 2R

Final Answer:
• R_f = 2R
• Frequency of oscillation f = 1/(2πRC)

Answer: Option (B) - 2R and 1/(2πRC)