In the circuit below, the opamp is ideal. If the circuit is to show sustained oscillations, the respective values of \(R_1\) and the corresponding frequency of oscillation are \(\_\_\_\_\).
Show Hint
In a Wien Bridge oscillator, verify that the gain condition (\(R_1/R = 2\)) is met, and use the RC feedback network to calculate the oscillation frequency accurately. Proper component selection ensures stable oscillations.
Step 1: Circuit analysis.
The given circuit is a Wien Bridge oscillator. To achieve sustained oscillations, the circuit must satisfy the Barkhausen criterion, which requires the loop gain to be exactly unity and the phase shift around the loop to be zero or an integer multiple of \(360^\circ\).
Step 2: Determine \(R_1\).
The gain condition for oscillations in a Wien Bridge oscillator is given by:
\[
\frac{R_1}{R} = 2.
\]
From this, we can calculate:
\[
R_1 = 2R.
\]
Step 3: Calculate the oscillation frequency.
The frequency of oscillation is determined by the components of the feedback network:
\[
f = \frac{1}{2\pi RC}.
\]
Final Answer:
\[
\boxed{{(2) } 2R \, {and} \, \frac{1}{2\pi RC}}
\]
