Question

Time constant of a C-R circuit is $\frac{2}{\ln \left(2\right)}s$. Capacitor is discharged at time $t=0$. The ratio of charge on the capacitor at time $t=2s$ and $t=6s$ is:

• A. $3:1$
• B. $8:1$
• C. $4:1$
• D. $2:1$

Answer 1

The correct option is C $4:1$

$Q=Q_0{e}^{\frac{-t}{\tau }}$

$Q_1=Q_0{e}^{\frac{-2}{2}ln2}=\frac{Q_0}{2}$

$Q_2=Q_0{e}^{\frac{-6}{2}ln2}=\frac{Q_0}{8}$

$\frac{Q_1}{Q_2}=4:1$