Opamp RC-circuit -- Capacitor time constant calculation

In summary: I really appreciate itIn summary, the opamp circuit sees the "-" terminal as a virtual ground and the feedback circuit can't "see" anything past that connection, so the input current is fixed by voltage source and input resistor only.
  • #1
Abdulwahab Hajar
56
2

Homework Statement


for the opamp circuit give in the figure, find Vo(t) for t > 0
the figure is attached.

Homework Equations


I know that tau = R * C
that is the time constant of a capacitor discharging is equal to the product of the resistor that it discharges through and its capacitance.

The Attempt at a Solution


The solution is in the file attached, I understand the whole thing. However, when I calculate the time constant my intuition tells me that the capactior discharges through the 100KΩ, the 20KΩ and the 10KΩ resistors. But the solution tells us that the 10KΩ resistor isn't included in the calculation of the time constant.
My question is why?

Thanks for the help
 

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  • #2
Consider the properties of an ideal op-amp. In your circuit, what's the potential at the - input of the op-amp?
 
  • #3
Yes, since it's an ideal op-amp the voltages of the - and + inputs of the opamps would be the same.
Therefore, the answer to your question would be: the voltage at the negative input would be 0V since the positive input is grounded and they must be equal.
But where does that lead me...?
Thank you sir, I really appreciate it
 
  • #4
Abdulwahab Hajar said:
Yes, since it's an ideal op-amp the voltages of the - and + inputs of the opamps would be the same.
Therefore, the answer to your question would be: the voltage at the negative input would be 0V since the positive input is grounded and they must be equal.
But where does that lead me...?
Thank you sir, I really appreciate it
The feedback circuit "sees" the "-" terminal as a virtual ground (fixed at 0 V). Essentially it can't "see" anything past that connection, as it's effectively "shorted out" by the virtual ground.
 
  • #5
But beyond that 0V there's a resistor of 10KΩ with 4V on the other end.
Doesn't that count for anything? I mean because a voltage difference exists shouldn't that incur a current somehow?
 
  • #6
Abdulwahab Hajar said:
But beyond that 0V there's a resistor of 10KΩ with 4V on the other end.
Doesn't that count for anything? I mean because a voltage difference exists shouldn't that incur a current somehow?
That fixed 0 V means that the source current cannot be influenced in any way by what happens to the capacitor voltage. The feedback circuit only sees the (virtual) ground connection. Similarly, the input voltage source only sees the same virtual ground (hence the input current is fixed by voltage source and input resistor only).

Remember how when you want to determine the Thevenin resistance for a network you suppress fixed voltage sources by replacing them with a short circuit? The fixed input voltage at the - terminal becomes a short to ground.
 
  • #7
Alright cool, I somehow got it
Thanks sir
 

FAQ: Opamp RC-circuit -- Capacitor time constant calculation

1. What is an Opamp RC-circuit?

An Opamp RC-circuit is a circuit that uses an operational amplifier (Opamp) and a resistor-capacitor (RC) network to perform various mathematical operations, such as amplification, filtering, and integration.

2. What is a Capacitor time constant?

A Capacitor time constant is a measure of how quickly a capacitor charges or discharges in an RC-circuit. It is calculated by multiplying the resistance (R) and capacitance (C) values in the circuit.

3. How do you calculate the time constant in an Opamp RC-circuit?

The time constant in an Opamp RC-circuit can be calculated by multiplying the resistance (R) and capacitance (C) values in the circuit. The formula is τ = R x C, where τ is the time constant in seconds, R is the resistance in ohms, and C is the capacitance in farads.

4. Why is the time constant important in an Opamp RC-circuit?

The time constant is important in an Opamp RC-circuit because it determines the rate of change of the output voltage. A shorter time constant means the output voltage changes more quickly, while a longer time constant means the output voltage changes more slowly.

5. How does the time constant affect the performance of an Opamp RC-circuit?

The time constant affects the performance of an Opamp RC-circuit in several ways. A shorter time constant allows for faster response times and better high-frequency performance, while a longer time constant allows for better low-frequency performance and more stable output voltage. The choice of time constant will depend on the specific application and desired performance of the circuit.

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