A2.1-mf capacitor is discharged through a 4.0-kω resistor. how long will it take for the capacitor to lose half its initial stored energy?

(a) 5.82 s
(b) 2.91 s
(c) 0.660 s
(d) 4.20 s
(e) 8.40 s

the answer is a)5.82s

Explanation:

Hello!

The first thing we must understand to solve this exercise is that a capacitor has the following characteristic function

where

Vo=initial voltage

V=voltage in an instant of time

t=time

R=resistance=4000Ω

C=capacitance=2.1-mF=0.0021F

we must consider that the final voltage is half of the initial voltage so we deduce the following equation

V=Vo/2

Now we replace in the initial equation, and start an algebraic process to find t

finally with the equation ready, we use the resistance and capacitance values to find the time value

the answer is a)5.82s

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