The electric current through a conductor is a flow of electric oriented charges.
If a capacitor is connected to a direct current source, it receives an electrical charge.
The value of the charge stored is obtained by multiplying the current delivered by the source and the time during which the source was connected to the capacitor.
Then:
Q = I x t (charge = current x time)
Where:
Q: charge in Coulombs
I: current in amperes
t: time in seconds
Experimentally, we can see that the charge stored in a capacitor is directly proportional to the voltage applied between its terminals.
Then: Q = C x V (charge = capacitance x voltage)
Where:
Q: charge in Coulombs
C: capacitance in farads
V: voltage in volts
Leveling the last equation with the first one we obtain: Q = I x t = C x V
Clearing out:
V = I x t / C
If the values of C (capacitance) and the current remained constant, the voltage "V" will be proportional to the time.
Then we can say that:
When a capacitor is charged with a constant current value, the voltage between its terminals is proportional to the charging time.
