# How long does it take to fully charge the capacitor? A capacitor with 4700*10^-6 F is attached to a 12 V power supply and is charged with a constant current I = 15 mA .

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When a voltage is applied across a capacitor, a current starts to flow which charges the capacitor. If Vs denotes the voltage of the source and the voltage of the capacitor is Vc, the current that flows is proportional to Vs - Vc. It is not possible to maintain this current at a constant level by using a constant voltage source.

A capacitor takes an infinite amount of time to get completely charged. Usually, when a capacitor is charged to 99% of its ideal capacity it is considered fully charged.

The charging of a capacitor can be analyzed by the time constant RC, where R is the resistance.

Here, I assume 15 mA is the initial current. This gives the resistance as R = V/I = 12/15*10^-3 = 12000/15 = 800 ohm

The time constant of the capacitor is given by RC = 800*4700*10^-6 = 3.76 s.

The capacitor is 99% charged after 5 time constants or 5*3.76 = 18.8 s.

The time taken to charge the capacitor to a level that is considered fully charged is 18.8 s.

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