An uncharged capacitor of capacitance 4 μ F and a resistance of 2 . 5 M Ω are connected in series with 12 V battery at t = 0 . Find the time in seconds after which the potential difference across the capacitor is 3 times the potential difference across the resistor. [Given, ln ( 2 ) = 0 . 693 ]

Step-by-step solution

Given :   V C   =   3 V R   =   3 ( V   -   V C ) Here, V is the applied potential. ∴     V C = 3 4   V o r     V ( 1 − e − t / T ) = 3 4   V ∴   e − t / τ   =   1 4 ⇒   t   =   τ   ln   4   =   2 τ   ln   2. Here τ   =   C R   = 10  s ⇒   t   =   2   ×   10