How do resistors affect capacitors?

When capacitors and resistors are connected together the resistor resists the flow of current that can charge or discharge the capacitor.
The larger the resistor , the slower the charge/discharge rate.
The larger the capacitor , the slower the charge/discharge rate.

If a voltage is applied to a capacitor through a series resistor, the charging current will be highest when the cap has 0 Volts across it.
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(i.e. when it is first connected the full voltage will be across the resistor).

The maximum charge current is limited to `I = V/R`
where `V` is the applied voltage and `R` is the series resistance.

The voltage on the capacitor changes as it charges or discharges.

As the capacitor charges the voltage across the resistor drops
(`V_R = V - V_"cap"`) so the current through it drops.

This results in a charge curve that starts off at it's maximum charge rate and tails off to a slower and slower charge rate as the capacitor nears its fully charged state.

(Image source: http://hyperphysics.phy-astr.gsu.edu/hbase/electric/capchg.html).

The same thing happens when discharging through a resistor, with maximum discharge at the beginning.

The time taken for a particular capacitor value to charge to 63.2% of full charge through a particular resistor value to is known as the "time constant" for the RC combination.

The time constant is always the same for the same RC values regardless of applied voltage.