How long will it take for a 22 $\mu \mathrm { F }$ capacitor to completely charge through a 47 $\mathrm { k } \Omega$ resistor?
A) 5.17 s
B) 8.272 s
C) 1.034 s
D) 2.068 s

Question

How long will it take for a 22 $\mu \mathrm { F }$ capacitor to completely charge through a 47 $\mathrm { k } \Omega$ resistor?
A)  5.17 s 
B)  8.272 s
C)  1.034 s
D)  2.068 s

Quizplus · Accepted Answer

The time it takes for a capacitor to charge through a resistor is determined by the time constant $\tau = RC$, where $R$ is the resistance in ohms and $C$ is the capacitance in farads. For a 22 $\mu \mathrm{F}$ capacitor and a 47 $\mathrm{k}\Omega$ resistor, $\tau = 47 \times 10^3 \Omega \times 22 \times 10^{-6} \mathrm{F} = 1.034 \mathrm{s}$. However, to fully charge a capacitor, it takes about 5 time constants, so the total time is $5 \times 1.034 \mathrm{s} = 5.17 \mathrm{s}$.

How Long Will It Take for a 22 μF\mu \mathrm { F }μF

How Long Will It Take for a 22 $\mu \mathrm { F }$