GATE Electrical Engineering (EE) 2018 Solved Paper

Question : 29 of 65

Marks: +1, -0

The op-amp shown in the figure is ideal. The input impedance is given by

Solution:

According to virtual ground

V_{+}=V_{-}=V_{i n}

By KVL

V_{0}=V_{i n}-I_{i n} Z

I_{i n}=\;{V_{i n}-V_{0}}/{Z}

.....(i)
Also by voltage division

V_{0}=V_{\;\text "in "\;}(\;{R_{1}}/{R_{2}}+1)

.....(ii)
Equation (ii) in equation (i)

I_{i n}=-\;{V_{i n} R_{1}}/{R_{2} Z}

Z_{\;\text "in "\;}=\;{V_{\;\text "in "\;}}/{l_{\;\text "in "\;}}=-Z \;{R_{2}}/{R_{1}}

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