(Solved): Consider the amplifier circuit shown below. Assume the operational amplifier is ideal, and that it ...

Consider the amplifier circuit shown below. Assume the operational amplifier is ideal, and that its supply voltages are \( \pm 20 \mathrm{~V} \). The magnitude of the gain of the amplifier circuit is 6 , and \( R_{2} \) is given to be \( 8 \mathrm{k} \Omega \) and \( R_{3}=2 \mathrm{k} \Omega \). (a) Find \( R_{1} \) that achieves the given amplifier gain. (b) Now assume that a \( 2 \mathrm{k} \Omega \) resistor is placed at the output terminals. The input signal is \[ v_{\text {in }}(t)=3 \sin (200 \pi t) \] Plot the output \( v_{\text {out }}(t) \) for \( 0 \leq t \leq 20 \mathrm{~ms} \).