The input voltage $${V_i}$$ in the circuit is a $$1$$ $$kHz$$ sine wave of $$1$$ $$V$$ amplitude. Assume ideal operational amplifiers with $$ \pm 15V\,\,DC$$ supply. Sketch on a single diagram the wave-forms of $${V_i},$$ $${V_1}$$ and $${V_0}$$ show, indicating the peak value of$${V_1}$$ and the average value $${V_0}$$.

In the circuit of figure $${R_s} = 2\,k\Omega ,$$ $${R_L} = 5\,k\Omega $$ For the op-amp $$A = {10^5},$$
$${R_i} = 100\,k\Omega ,\,\,{R_0} = 50\,k\Omega .$$ For $${V_0} = 10V.$$
Calculate $${V_S}$$ and $${{{V_0}} \over {{V_S}}}$$ and estimate the input resistance of the circuit,

Figure below shows an op-amp amplifier. Find the output voltage in steady state condition where $$(i)$$ switch is open $$(ii)$$ $$S$$ is closed

$$(a)$$ For the circuit shown in figure

$$(i)$$ Calculate the transfer function $${{{V_0}} \over {{V_i}}}$$
$$(ii)$$ plot the amplitude and phase response as a function for $$R = {R_1}$$