What are the conditions for an RC circuit to work as an integrator/differentiator Can you derive it with this circuit

Question

Accepted Answer

RC circuit works as integrator/differentiator under certain conditions. Can be derived with circuit analysis.

For an RC circuit to work as an integrator, the time constant (RC) should be large enough compared to the input signal frequency.
For an RC circuit to work as a differentiator, the time constant (RC) should be small enough compared to the input signal frequency.
The output voltage of an RC integrator circuit is proportional to the integral of the input voltage.
The output voltage of an RC differentiator circuit is proportional to the derivative of the input voltage.
The circuit can be analyzed using Laplace transforms to derive the conditions for integration/differentiation.

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