Question

In the circuit using Zener diode and ideal opamp with $V_Z=2.5$ V as shown below, an unit step input voltage is applied i.e. $V_{IN}\left(t\right)=u\left(t\right)$ V. Also it is given the voltage across each of the capacitors is zero then time, t in milliseconds at which the output voltage $V_{out}$ crosses - 10 V is ______m sec.

• A. 7.5

Answer 1

The correct option is A 7.5
For given configuration assuming current I in capacitor branch,


For t > 0, $I=\frac{1V}{1k\Omega }=1mA$

The capacitor charges with constant current I and both $V_1$ and $V_2$ will increase till $V_2$ reaches 2.5 V. At this $V_2$ remains at 2.5 V and $V_1$ increases with time

$V_{out}\left(t\right)=-10V$

$V_1=7.5V$

So, $\frac{1}{c}{\int }_0^{t}Idt=\frac{1}{1\times {10}^{-6}}{\int }_0^t{10}^{-3}dt$

$\frac{{10}^{-3}}{{10}^{-6}}t=7.5$

$t=7.5msec$