For the oscillator circuit shown in figure, the expression for the time period of oscillations can be given by (where $$\tau = RC$$ )

For the op-amp circuit shown in figure. Determine the output voltage $${v_0}.$$ Assume that the op-amps are ideal

A simple active filter is shown in figure. Assume ideal op-amp. Derive the transfer function $${v_0}/{v_i}$$ of the circuit, and state the type of the filter (i.e., high-pass, low-pass, band-pass, or band-reject). Determine the required values of $${R_1},{R_2}$$ and $$C$$ in order for the filter to have a $$3$$-$$dB$$ frequency of $$1$$ $$kHz,$$ a high frequency input resistance of $$100\,\,k\Omega $$ and a high frequency gain magnitude of $$10.$$

An op-amp has an open-loop gain of $${10^5}$$ and an open-loop upper cutoff frequency of $$10$$ $$Hz.$$ If this op-amp is connected as an amplifier with a closed-loop gain of $$100,$$ then the new upper cutoff frequency is