First slide

electric current

Question

A 4 μFcapacitor and a resistance of 2.5 M $Ω$ are in series with 12V battery. Find the time after which the potential difference across the capacitor is 3 times the potential difference across the resistor :

Easy

A

5 ln 4
B

10 ln 4
C

20 ln 4
D

40 ln 2

Solution

$V_{C} = 3 V_{R} = 3 (E - V_{C})$
$\Rightarrow V_{C} = \frac{3 E}{4} = E (1 - e^{- t / RC}) \Rightarrow e^{- t / RC} = \frac{1}{4} \Rightarrow e^{t / RC} = 4 \Rightarrow \frac{t}{RC} = \ln 4 \Rightarrow t = RC \ln 4$

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