# How to solve OP-amp capacitor circuit?

#### zenos123

May 9, 2020
2
Hi, I am currently struggling with this questions. i will appreciate any help thanks.

Consider the following first-order circuit bellowwhere =4() and (0)=1 V. Determine the voltage () and the current () for t > 0.

#### Harald Kapp

##### Moderator
Moderator
Nov 17, 2011
12,735
I moved your thread to the homeworks section where we deal with such questions.
First you have to:
1. Clarify what this means:
circuit bellowwhere =4() and (0)=1 V.
That makes absolutely no sense to me.

2. Show us what you have done so far to solve the task.

#### zenos123

May 9, 2020
2
Hi, I am currently struggling with this question.

Consider the following first-order circuit in Figure 4 where vs=4u(t) and v(0)=1 V. Determine the voltage v0(t) and the current i0(t) for t > 0.

I see that OP amp is connected to voltage source, which mean that minus pin of the OP-amp and its positive pin will have the same voltage. This means that 20k ohm resistor and capacitor parallel to the 10k ohm resistor will have initial voltage of vs or 1v. Now, I am not sure what to do next. Do I need to look for the voltage drop using t>0? what is the point of initial condition v(0)=1V?

#### Nanren888

Nov 8, 2015
623
Examine the path that i0 takes.

It seems if the source is a unit step times 4.0 then the input becomes 4.0 at t=0;
If, as you say the two opamp inputs are equal then you can work out the current through the 20K resistor.
If the opamp is perfect, infinite input impedance, then you can calculate the current elsewhere too.
.
The voltage across a capacitor has an integral in the formulation. Any integral remains indefinite until some initial condition is added to allow the constant to be fixed, specified. To solve to vo(t) without an unknown constant, you'll need that constant.

Moderator
Nov 17, 2011
12,735

#### Ratch

Mar 10, 2013
1,098
Hi, I am currently struggling with this question.

Consider the following first-order circuit in Figure 4 where vs=4u(t) and v(0)=1 V. Determine the voltage v0(t) and the current i0(t) for t > 0.
View attachment 48145
I see that OP amp is connected to voltage source, which mean that minus pin of the OP-amp and its positive pin will have the same voltage. This means that 20k ohm resistor and capacitor parallel to the 10k ohm resistor will have initial voltage of vs or 1v. Now, I am not sure what to do next. Do I need to look for the voltage drop using t>0? what is the point of initial condition v(0)=1V?

At t=0, the left side of the RC combo will measure 4 volts ( vs=4u(t) ) and the right side will measure 1 volt (v(0)=1) for a difference of 3 volts. As the energy storage characteristics of the capacitor and the amplification of the opamp come into play, the voltages and currents will change accordingly at t>0. Because you have a single energy storage element (capacitor), you will be dealing with a first order differential equation (DE). You must either write a loop or node equation and solve this DE. The Laplace method is the quickest and easiest way to do this.
Ratch

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