How fast can a capacitor charge?

Hint: A capacitor is an electronic component used to store energy in the form of an electric field. It is used in those electronic devices which need a large amount of energy to start initially. A capacitor connected to a battery in a circuit charges till the time the voltage across the capacitor is developed and gets equal to the voltage of the battery.

Complete answer:
Generally, charging a capacitor fully takes infinite time.
While discussing the charging and discharging of a capacitor, we must know about a term called the time constant. The time constant of a capacitor is defined as the product of resistance and capacitance of the capacitor. The capacitor charges to \[63\% \] in one constant of time of the capacitor. To charge the capacitor by \[99\% \] , a time of five times constant is taken. But after \[99\% \] charging capacitor takes infinite time to fully charge.
Hence, the time taken to charge the capacitor by \[99\% \] is five times its time constant, but to charge it fully will take infinite time.

Note:
Suppose the capacitance of a capacitor is $200\mu F$, the resistance across the circuit is $2k\Omega $, and the battery of $5V$. Then the time taken to charge this capacitor \[99\% \] is calculated below. Time $ = 5\left( {200\mu \times 2k} \right) = 2\sec $
So the time taken to charge it by \[99\% \] is only two seconds but after this time taken to charge the remaining 1% takes infinite. Or we can say that the capacitor can never be charged \[100\% \] .