An uncharged capacitor of capacitance 4 µF, a 12 V battery and a 2.5 MΩ resistor are connected in series. Find the time after which the capacitor voltage is three times the resistor voltage. Take ln 2 = 0.693.
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Question

An uncharged capacitor of capacitance 4 µF, a 12 V battery and a 2.5 MΩ resistor are connected in series. Find the time after which the capacitor voltage is three times the resistor voltage. Take ln 2 = 0.693.

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G1 Physics · Accepted Answer

Here τ = RC = (2.5 MΩ)(4 µF) = 10 s. During charging, capacitor voltage = E(1−e^(−t/τ)) and resistor voltage = Ee^(−t/τ). Setting capacitor voltage = 3 × resistor voltage gives e^(−t/τ) = 1/4, so t = τ ln 4 = 13.86 s. Hence B.