Question

A capacitor C is connected to two equal resistances as shown in the figure. Consider the following statements:
(i) At the time of charging of capacitor time constant of the circuit is 2CR
(ii) At the time of discharging of the capacitor the time constant of the circuit is CR
(iii) At the time of discharging of the capacitor the time constant of the circuit is 2CR
(iv) At the time of charging of capacitor the time constant of the circuit is CR

• A. Statements (i) and (ii) only are correct
• B. Statements (ii) and (iii) only are correct
• C. Statements (iii) and (iv) only are correct
• D. Statements (i) and (iii) only are correct

Answer 1

The correct option is C Statements (iii) and (iv) only are correct

Here 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: $\tau =CR$
Here the 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: ${\tau }^{\prime }=C{R}_{net}=2CR$