How long does it take to fully charge the capacitor in the following case:

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

Give the result in seconds accurate to 2 significant places.

Expert Answers

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A capacitor with a capacitance C attached in an RC circuit charges slowly and there is a buildup of a voltage between its plates. It is not possible to fully charge a capacitor. We can only approach a fully charged state by passing current through the circuit in which the capacitor is placed over an adequate duration of time.

After a time equal to 5*RC a steady stead condition is reached and the capacitor is considered fully charged.

Here it is given that the voltage across the capacitor is 12V, it has a capacitance of 4700 micro farad, and a constant current of 15 mA is used to charge it.

The current can be used to calculate the resistance R = V/I = 12/15*10^-3 = 12000/15 = 800 kilo ohm.

The time constant of the capacitor is RC = 800 * 10^3 * 4700 * 10^-6

=> 3760 s.

5*RC = 18800 s.

The time taken to charge the capacitor to approach a steady state condition is 18800 seconds.

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