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 ]

Question

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 ],

MARKS App · Accepted Answer

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 × 0.693 = 13 .86 s

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