GATE 2015 EE – SET 1 – Question 39

Solution :

$$V_{0} $$= A$$(V_{+}-V_{-}) $$

$$V_{0} $$= 1000(0-$$V_{A}$$)

$$V_{0} $$= -1000 $$V_{A}$$

KCL at A ,
$$\frac{V_{A}-V_{i}}{1000} – \frac{V_{A}-V_{0}}{X_{C}} $$= 0

$$\frac{V_{A}-V_{i}}{1000}$$ =$$\frac{V_{A}-(-1000V_{A})}{\frac{1}{SC}}$$

$$V_{A}-V_{i} $$=(1000)$$\left [ V_{A} +1000V_{A}\right ]SC$$

$$V_{A}-V_{i} $$ = (1001)*$$10^{3}$$*SC $$\left [ V_{A} \right ]$$

$$V_{A}-V_{i} $$ = (1001)*$$10^{3}$$* 1* $$10^{-6}$$

⇒ 1001 -10^-{3}  ⇒ 1.001s = 1001ms