Question

A capacitor $C$ is connected to the two equal resistances as shown in the figure. What is the ratio of time constant during charging and discharging of the capacitance ?

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

Answer 1

The correct option is C $1:2$

$\text{During the charging:}$The capacitor will charge through the resistor on right side only and during charging the middle resistor will not be working.


Thus, the time constant during charging is: ${\tau }_1=C{R}_{net}=CR$

$\text{During the discharging}:$ capacitor will discharge through both resistances.



The resistances are in series so net resistance is $R_{net}=R+R=2R$
Thus, the times constant during discharging is: ${\tau }_2=C{R}_{net}=2CR$

Ratio of the time constants:

$\frac{{\tau }_1}{{\tau }_2}=1:2$

Hence, option (c) is correct answer.