Answer:
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
[tex]V=(Vo)e^{-t/RC}[/tex]
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
[tex]\frac{Vo}{2} =(Vo)e^{-t/RC}\\0.5=e^{-t/RC}\\ln(0.5)=ln(e^{-t/RC})\\ln(0.5)=\frac{-t}{RC} \\t=-(RC)ln0.5[/tex]
finally with the equation ready, we use the resistance and capacitance values to find the time value
[tex]t=-(4000)(0.0021)ln(0.5)=5.82s[/tex]
the answer is a)5.82s
