What causes integration of V_in in an RC circuit?

[wetlife]

Homework Statement

What causes integration of V_{in} within an RC circuit?

Homework Equations

Z= R + X_C
= R - j/(ωC)

Z is the impedance of the circuit, j=(-1)^.5, ω is angular frequency, and C is the capacitance.

The Attempt at a Solution

I think integration is the capacitor's way of "remembering" how much energy it has to put back into the circuit.

 

[berkeman]

Homework Statement

What causes integration of V_{in} within an RC circuit?

Homework Equations

Z= R + X_C
= R - j/(ωC)

Z is the impedance of the circuit, j=(-1)^.5, ω is angular frequency, and C is the capacitance.

The Attempt at a Solution

I think integration is the capacitor's way of "remembering" how much energy it has to put back into the circuit.

For this question, it is probably best to stay in the time domain, and just start with the differential equation that relates current and voltage for a capacitor. Can you show us that equation and suggest how you can use it to answer this question?