Assertion:- Time constants of the cirucits shown in the figure are same.

Reason:- Instantaneous current through the capacitor branch is same at any instant for both the circuits, if batteries are inserted in the circuits at `t=0`

Options

A. If both Assertion `&` Reason are True `&` the Reason is a correct explanation of the Assertion.
B. If both Assertion `&` Reason are True but Reason is not a correct explanation of the Assertion.
C. If Assertion is True but the Reason is False.
D. If both Assertion `&` Reason are False.

Answer

C

Explanation

`t=(CR_(1)R_(2))/(R_(1)+R_(2))`
`I_("Initial")=(V_(0)(R_(1)+R_(2)))/(R_(1)R_(2))`
`I_("Initial")` across resistance
`I_("initial")` across capacitor
`=(V_(0)(R_(1)+R(2)))/(R_(1)R_(2)))`

`tau=(CR_(1)R_(2))/(R_(1)+R_(2))`
short the battery and R across capacitor
`=R_(eq)=(R_(1)R_(2))/(R_(1)+R_(2))`
`I_("Initial")=(V_(0))/(R_(1))`
`I_(("capacitor")"initial")=(V_(0))/(R_(1))`