The GATE Grind

GATE 2015 EE – Question 49

Analog and Digital Electronics · Operational amplifiers: characteristics and applications · 2 marks · Multiple choice

The op-amp shown in the figure has a finite gain $A = 1000$ and an infinite input resistance. A step-voltage $V_i = 1$ mV is applied at the input at time $t = 0$ as shown. Assuming that the operational amplifier is not saturated, the time constant (in millisecond) of the output voltage $V_o$ is

An inverting amplifier with a $1\ \text{k}\Omega$ input resistor and a $1\ \mu\text{F}$ capacitor in the feedback path, around an op-amp of gain $A = 1000$.
  1. 1001
  2. 101
  3. 11
  4. 1

Practise this question in The GATE Grind →

Show answer and explanation

Correct answer: (A) 1001

Explanation

In an integrator with finite gain $A$, the Miller effect multiplies the capacitor by $(1 + A)$, so the time constant is $(1 + A)RC = 1001 \times 1\ \text{k}\Omega \times 1\ \mu\text{F} = 1.001$ s, which is 1001 ms.