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Imagine the frequency behavior of the series combination of R and C. For low frequencies it is the cap impedance that dominates. At high frequencies it is the R. This can be decomposed as an integrator type of responce from the cap only and a response that has a zero at 1/RC as in the drawing.
The response of current and voltage in a circuit immediately after a change in applied voltage is called the transient response. A circuit that contains resistance and capacitance is called an RC circuit.