Charging of capacitor in RC circuit
simulate this circuit &ndash; Schematic created using CircuitLab
The current is determined by the voltage across the resistor, which is V1-Vc. As the capacitor charges, Vc increases while V1 stays the same, so the current decreases. The rate at which a capacitor charges is directly proportional to the current, so the rate at which it charges decreases proportional to its current state of charge--the classic differential equation for an exponential decay.